diff --git a/ignite/contrib/engines/common.py b/ignite/contrib/engines/common.py
index 76c25e2b..a4833e50 100644
--- a/ignite/contrib/engines/common.py
+++ b/ignite/contrib/engines/common.py
@@ -4,6 +4,7 @@ from collections.abc import Mapping, Sequence
 from functools import partial
 
 import torch
+import torch.nn as nn
 from torch.utils.data.distributed import DistributedSampler
 
 import ignite.distributed as idist
@@ -40,6 +41,8 @@ def setup_common_training_handlers(
     device=None,
     stop_on_nan=True,
     clear_cuda_cache=True,
+    save_handler=None,
+    **kwargs
 ):
     """Helper method to setup trainer with common handlers (it also supports distributed configuration):
         - :class:`~ignite.handlers.TerminateOnNan`
@@ -57,7 +60,8 @@ def setup_common_training_handlers(
             :class:`~ignite.handlers.Checkpoint` instance.
         save_every_iters (int, optional): saving interval. By default, `to_save` objects are stored
             each 1000 iterations.
-        output_path (str, optional): output path to indicate where `to_save` objects are stored.
+        output_path (str, optional): output path to indicate where `to_save` objects are stored. Argument is mutually
+            exclusive with ``save_handler``.
         lr_scheduler (ParamScheduler or subclass of `torch.optim.lr_scheduler._LRScheduler`): learning rate scheduler
             as native torch LRScheduler or ignite's parameter scheduler.
         with_gpu_stats (bool, optional): if True, :class:`~ignite.contrib.metrics.handlers.GpuInfo` is attached to the
@@ -73,12 +77,16 @@ def setup_common_training_handlers(
             Default, True.
         clear_cuda_cache (bool, optional): if True, `torch.cuda.empty_cache()` is called every end of epoch.
             Default, True.
+        save_handler (callable or :class:`~ignite.handlers.checkpoint.BaseSaveHandler`, optional): Method or callable
+            class to use to store ``to_save``. See :class:`~ignite.handlers.checkpoint.Checkpoint` for more details.
+            Argument is mutually exclusive with ``output_path``.
+        **kwargs: optional keyword args to be passed to construct :class:`~ignite.handlers.checkpoint.Checkpoint`.
         device (str of torch.device, optional): deprecated argument, it will be removed in v0.5.0.
     """
     if device is not None:
         warnings.warn("Argument device is unused and deprecated. It will be removed in v0.5.0")
 
-    kwargs = dict(
+    _kwargs = dict(
         to_save=to_save,
         save_every_iters=save_every_iters,
         output_path=output_path,
@@ -90,10 +98,12 @@ def setup_common_training_handlers(
         log_every_iters=log_every_iters,
         stop_on_nan=stop_on_nan,
         clear_cuda_cache=clear_cuda_cache,
+        save_handler=save_handler,
     )
+    _kwargs.update(kwargs)
 
     if idist.get_world_size() > 1:
-        _setup_common_distrib_training_handlers(trainer, train_sampler=train_sampler, **kwargs)
+        _setup_common_distrib_training_handlers(trainer, train_sampler=train_sampler, **_kwargs)
     else:
         if train_sampler is not None and isinstance(train_sampler, DistributedSampler):
             warnings.warn(
@@ -102,7 +112,7 @@ def setup_common_training_handlers(
                 "Train sampler argument will be ignored",
                 UserWarning,
             )
-        _setup_common_training_handlers(trainer, **kwargs)
+        _setup_common_training_handlers(trainer, **_kwargs)
 
 
 setup_common_distrib_training_handlers = setup_common_training_handlers
@@ -121,7 +131,14 @@ def _setup_common_training_handlers(
     log_every_iters=100,
     stop_on_nan=True,
     clear_cuda_cache=True,
+    save_handler=None,
+    **kwargs
 ):
+    if output_path is not None and save_handler is not None:
+        raise ValueError(
+            "Arguments output_path and save_handler are mutually exclusive. Please, define only one of them"
+        )
+
     if stop_on_nan:
         trainer.add_event_handler(Events.ITERATION_COMPLETED, TerminateOnNan())
 
@@ -137,11 +154,15 @@ def _setup_common_training_handlers(
         trainer.add_event_handler(Events.EPOCH_COMPLETED, empty_cuda_cache)
 
     if to_save is not None:
-        if output_path is None:
-            raise ValueError("If to_save argument is provided then output_path argument should be also defined")
-        checkpoint_handler = Checkpoint(
-            to_save, DiskSaver(dirname=output_path, require_empty=False), filename_prefix="training",
-        )
+
+        if output_path is None and save_handler is None:
+            raise ValueError(
+                "If to_save argument is provided then output_path or save_handler arguments should be also defined"
+            )
+        if output_path is not None:
+            save_handler = DiskSaver(dirname=output_path, require_empty=False)
+
+        checkpoint_handler = Checkpoint(to_save, save_handler, filename_prefix="training", **kwargs)
         trainer.add_event_handler(Events.ITERATION_COMPLETED(every=save_every_iters), checkpoint_handler)
 
     if with_gpu_stats:
@@ -192,6 +213,8 @@ def _setup_common_distrib_training_handlers(
     log_every_iters=100,
     stop_on_nan=True,
     clear_cuda_cache=True,
+    save_handler=None,
+    **kwargs
 ):
 
     _setup_common_training_handlers(
@@ -207,6 +230,8 @@ def _setup_common_distrib_training_handlers(
         log_every_iters=log_every_iters,
         stop_on_nan=stop_on_nan,
         clear_cuda_cache=clear_cuda_cache,
+        save_handler=save_handler,
+        **kwargs,
     )
 
     if train_sampler is not None:
@@ -450,19 +475,29 @@ def get_default_score_fn(metric_name):
     return wrapper
 
 
-def save_best_model_by_val_score(output_path, evaluator, model, metric_name, n_saved=3, trainer=None, tag="val"):
-    """Method adds a handler to `evaluator` to save best models based on the score (named by `metric_name`)
-    provided by `evaluator`.
+def gen_save_best_models_by_val_score(
+    save_handler, evaluator, models, metric_name, n_saved=3, trainer=None, tag="val", **kwargs
+):
+    """Method adds a handler to ``evaluator`` to save ``n_saved`` of best models based on the metric
+    (named by ``metric_name``) provided by ``evaluator`` (i.e. ``evaluator.state.metrics[metric_name]``).
+    The logic of how to store objects is delegated to ``save_handler``.
 
     Args:
-        output_path (str): output path to indicate where to save best models
+        save_handler (callable or :class:`~ignite.handlers.checkpoint.BaseSaveHandler`): Method or callable class to
+            use to save engine and other provided objects. Function receives two objects: checkpoint as a dictionary
+            and filename. If ``save_handler`` is callable class, it can
+            inherit of :class:`~ignite.handlers.checkpoint.BaseSaveHandler` and optionally implement ``remove`` method
+            to keep a fixed number of saved checkpoints. In case if user needs to save engine's checkpoint on a disk,
+            ``save_handler`` can be defined with :class:`~ignite.handlers.DiskSaver`.
         evaluator (Engine): evaluation engine used to provide the score
-        model (nn.Module): model to store
+        models (nn.Module or Mapping): model or dictionary with the object to save. Objects should have
+            implemented ``state_dict`` and ``load_state_dict`` methods.
         metric_name (str): metric name to use for score evaluation. This metric should be present in
             `evaluator.state.metrics`.
         n_saved (int, optional): number of best models to store
         trainer (Engine, optional): trainer engine to fetch the epoch when saving the best model.
         tag (str, optional): score name prefix: `{tag}_{metric_name}`. By default, tag is "val".
+        **kwargs: optional keyword args to be passed to construct :class:`~ignite.handlers.checkpoint.Checkpoint`.
 
     Returns:
         A :class:`~ignite.handlers.checkpoint.Checkpoint` handler.
@@ -471,14 +506,19 @@ def save_best_model_by_val_score(output_path, evaluator, model, metric_name, n_s
     if trainer is not None:
         global_step_transform = global_step_from_engine(trainer)
 
+    to_save = models
+    if isinstance(models, nn.Module):
+        to_save = {"model": models}
+
     best_model_handler = Checkpoint(
-        {"model": model,},
-        DiskSaver(dirname=output_path, require_empty=False),
+        to_save,
+        save_handler,
         filename_prefix="best",
         n_saved=n_saved,
         global_step_transform=global_step_transform,
         score_name="{}_{}".format(tag, metric_name.lower()),
         score_function=get_default_score_fn(metric_name),
+        **kwargs,
     )
     evaluator.add_event_handler(
         Events.COMPLETED, best_model_handler,
@@ -487,6 +527,38 @@ def save_best_model_by_val_score(output_path, evaluator, model, metric_name, n_s
     return best_model_handler
 
 
+def save_best_model_by_val_score(
+    output_path, evaluator, model, metric_name, n_saved=3, trainer=None, tag="val", **kwargs
+):
+    """Method adds a handler to ``evaluator`` to save on a disk ``n_saved`` of best models based on the metric
+    (named by ``metric_name``) provided by ``evaluator`` (i.e. ``evaluator.state.metrics[metric_name]``).
+
+    Args:
+        output_path (str): output path to indicate where to save best models
+        evaluator (Engine): evaluation engine used to provide the score
+        model (nn.Module): model to store
+        metric_name (str): metric name to use for score evaluation. This metric should be present in
+            `evaluator.state.metrics`.
+        n_saved (int, optional): number of best models to store
+        trainer (Engine, optional): trainer engine to fetch the epoch when saving the best model.
+        tag (str, optional): score name prefix: `{tag}_{metric_name}`. By default, tag is "val".
+        **kwargs: optional keyword args to be passed to construct :class:`~ignite.handlers.checkpoint.Checkpoint`.
+
+    Returns:
+        A :class:`~ignite.handlers.checkpoint.Checkpoint` handler.
+    """
+    return gen_save_best_models_by_val_score(
+        save_handler=DiskSaver(dirname=output_path, require_empty=False),
+        evaluator=evaluator,
+        models=model,
+        metric_name=metric_name,
+        n_saved=n_saved,
+        trainer=trainer,
+        tag=tag,
+        **kwargs,
+    )
+
+
 def add_early_stopping_by_val_score(patience, evaluator, trainer, metric_name):
     """Method setups early stopping handler based on the score (named by `metric_name`) provided by `evaluator`.
 

diff --git a/tests/ignite/contrib/engines/test_common.py b/tests/ignite/contrib/engines/test_common.py
index 2b17af87..8d9a8ee7 100644
--- a/tests/ignite/contrib/engines/test_common.py
+++ b/tests/ignite/contrib/engines/test_common.py
@@ -1,6 +1,6 @@
 import os
 import sys
-from unittest.mock import MagicMock
+from unittest.mock import MagicMock, call
 
 import pytest
 import torch
@@ -12,6 +12,7 @@ import ignite.distributed as idist
 from ignite.contrib.engines.common import (
     _setup_logging,
     add_early_stopping_by_val_score,
+    gen_save_best_models_by_val_score,
     save_best_model_by_val_score,
     setup_any_logging,
     setup_common_training_handlers,
@@ -24,7 +25,7 @@ from ignite.contrib.engines.common import (
     setup_wandb_logging,
 )
 from ignite.engine import Engine, Events
-from ignite.handlers import TerminateOnNan
+from ignite.handlers import DiskSaver, TerminateOnNan
 
 
 class DummyModel(nn.Module):
@@ -36,7 +37,9 @@ class DummyModel(nn.Module):
         return self.net(x)
 
 
-def _test_setup_common_training_handlers(dirname, device, rank=0, local_rank=0, distributed=False, lr_scheduler=None):
+def _test_setup_common_training_handlers(
+    dirname, device, rank=0, local_rank=0, distributed=False, lr_scheduler=None, save_handler=None
+):
 
     lr = 0.01
     step_size = 100
@@ -86,6 +89,7 @@ def _test_setup_common_training_handlers(dirname, device, rank=0, local_rank=0,
         to_save={"model": model, "optimizer": optimizer},
         save_every_iters=75,
         output_path=dirname,
+        save_handler=save_handler,
         lr_scheduler=lr_scheduler,
         with_gpu_stats=False,
         output_names=["batch_loss",],
@@ -107,6 +111,8 @@ def _test_setup_common_training_handlers(dirname, device, rank=0, local_rank=0,
 
     # Check saved checkpoint
     if rank == 0:
+        if save_handler is not None:
+            dirname = save_handler.dirname
         checkpoints = list(os.listdir(dirname))
         assert len(checkpoints) == 1
         for v in [
@@ -124,10 +130,14 @@ def test_asserts_setup_common_training_handlers():
     trainer = Engine(lambda e, b: None)
 
     with pytest.raises(
-        ValueError, match=r"If to_save argument is provided then output_path argument should be also defined"
+        ValueError,
+        match=r"If to_save argument is provided then output_path or save_handler arguments should be also defined",
     ):
         setup_common_training_handlers(trainer, to_save={})
 
+    with pytest.raises(ValueError, match=r"Arguments output_path and save_handler are mutually exclusive"):
+        setup_common_training_handlers(trainer, to_save={}, output_path="abc", save_handler=lambda c, f, m: None)
+
     with pytest.warns(UserWarning, match=r"Argument train_sampler is a distributed sampler"):
         train_sampler = MagicMock(spec=DistributedSampler)
         setup_common_training_handlers(trainer, train_sampler=train_sampler)
@@ -167,10 +177,23 @@ def test_setup_common_training_handlers(dirname, capsys):
     out = captured.err.split("\r")
     out = list(map(lambda x: x.strip(), out))
     out = list(filter(None, out))
-    assert "Epoch:" in out[-1], "{}".format(out[-1])
+    assert "Epoch" in out[-1] or "Epoch" in out[-2], "{}, {}".format(out[-2], out[-1])
+
+
+def test_setup_common_training_handlers_using_save_handler(dirname, capsys):
+
+    save_handler = DiskSaver(dirname=dirname, require_empty=False)
+    _test_setup_common_training_handlers(dirname=None, device="cpu", save_handler=save_handler)
+
+    # Check epoch-wise pbar
+    captured = capsys.readouterr()
+    out = captured.err.split("\r")
+    out = list(map(lambda x: x.strip(), out))
+    out = list(filter(None, out))
+    assert "Epoch" in out[-1] or "Epoch" in out[-2], "{}, {}".format(out[-2], out[-1])
 
 
-def test_save_best_model_by_val_score(dirname, capsys):
+def test_save_best_model_by_val_score(dirname):
 
     trainer = Engine(lambda e, b: None)
     evaluator = Engine(lambda e, b: None)
@@ -180,9 +203,7 @@ def test_save_best_model_by_val_score(dirname, capsys):
 
     @trainer.on(Events.EPOCH_COMPLETED)
     def validate(engine):
-        evaluator.run(
-            [0,]
-        )
+        evaluator.run([0, 1])
 
     @evaluator.on(Events.EPOCH_COMPLETED)
     def set_eval_metric(engine):
@@ -190,12 +211,49 @@ def test_save_best_model_by_val_score(dirname, capsys):
 
     save_best_model_by_val_score(dirname, evaluator, model, metric_name="acc", n_saved=2, trainer=trainer)
 
-    data = [
-        0,
-    ]
-    trainer.run(data, max_epochs=len(acc_scores))
+    trainer.run([0, 1], max_epochs=len(acc_scores))
 
-    assert set(os.listdir(dirname)) == set(["best_model_8_val_acc=0.6100.pt", "best_model_9_val_acc=0.7000.pt"])
+    assert set(os.listdir(dirname)) == {"best_model_8_val_acc=0.6100.pt", "best_model_9_val_acc=0.7000.pt"}
+
+
+def test_gen_save_best_models_by_val_score():
+
+    trainer = Engine(lambda e, b: None)
+    evaluator = Engine(lambda e, b: None)
+    model = DummyModel()
+
+    acc_scores = [0.1, 0.2, 0.3, 0.4, 0.3, 0.5, 0.6, 0.61, 0.7, 0.5]
+
+    @trainer.on(Events.EPOCH_COMPLETED)
+    def validate(engine):
+        evaluator.run([0, 1])
+
+    @evaluator.on(Events.EPOCH_COMPLETED)
+    def set_eval_metric(engine):
+        engine.state.metrics = {"acc": acc_scores[trainer.state.epoch - 1]}
+
+    save_handler = MagicMock()
+
+    gen_save_best_models_by_val_score(
+        save_handler, evaluator, {"a": model, "b": model}, metric_name="acc", n_saved=2, trainer=trainer
+    )
+
+    trainer.run([0, 1], max_epochs=len(acc_scores))
+
+    assert save_handler.call_count == len(acc_scores) - 2  # 2 score values (0.3 and 0.5) are not the best
+    print(save_handler.mock_calls)
+    obj_to_save = {"a": model.state_dict(), "b": model.state_dict()}
+    save_handler.assert_has_calls(
+        [
+            call(
+                obj_to_save,
+                "best_checkpoint_{}_val_acc={:.4f}.pt".format(e, p),
+                dict([("basename", "best_checkpoint"), ("score_name", "val_acc"), ("priority", p)]),
+            )
+            for e, p in zip([1, 2, 3, 4, 6, 7, 8, 9], [0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.61, 0.7])
+        ],
+        any_order=True,
+    )
 
 
 def test_add_early_stopping_by_val_score():
@@ -206,9 +264,7 @@ def test_add_early_stopping_by_val_score():
 
     @trainer.on(Events.EPOCH_COMPLETED)
     def validate(engine):
-        evaluator.run(
-            [0,]
-        )
+        evaluator.run([0, 1])
 
     @evaluator.on(Events.EPOCH_COMPLETED)
     def set_eval_metric(engine):
@@ -216,10 +272,7 @@ def test_add_early_stopping_by_val_score():
 
     add_early_stopping_by_val_score(patience=3, evaluator=evaluator, trainer=trainer, metric_name="acc")
 
-    data = [
-        0,
-    ]
-    state = trainer.run(data, max_epochs=len(acc_scores))
+    state = trainer.run([0, 1], max_epochs=len(acc_scores))
 
     assert state.epoch == 7
 
@@ -259,9 +312,7 @@ def _test_setup_logging(
 
         @trainer.on(Events.EPOCH_COMPLETED)
         def validate(engine):
-            evaluator.run(
-                [0,]
-            )
+            evaluator.run([0, 1])
 
         @evaluator.on(Events.EPOCH_COMPLETED)
         def set_eval_metric(engine):

Improve usage of contrib common methods with other save handlers
## 🚀 Feature

Currently, methods like `common.save_best_model_by_val_score` and `common.setup_common_training_handlers` work with local storage setup by `output_path`.

If we would like to use other save handlers than `DiskSaver`, it is almost impossible to use those helpers.

Idea is to be able user's setup of save handler for internal `Checkpoint` class. 
There can be several ways, I see, how to accomplish that:
- make `output_path` accept instances of `BaseSaveHandler`

```python
from ignite.contrib.engines import common

save_handler = TrainsSaver(dirname=output_path)

common.save_best_model_by_val_score(
        save_handler, evaluator, model=model, metric_name="accuracy", n_saved=3, trainer=trainer, tag="test"
)
```

- set module-wise default save handler as DiskSaver and allow user to replace it by another save hander:

```python
from ignite.contrib.engines import common

common.default_save_handler = TrainsSaver(dirname=output_path)

common.save_best_model_by_val_score(
        None, evaluator, model=model, metric_name="accuracy", n_saved=3, trainer=trainer, tag="test"
)
```

- add another argument `save_handler=None`

```python
save_handler = TrainsSaver(dirname=output_path)

common.save_best_model_by_val_score(
        None, evaluator, model=model, metric_name="accuracy", n_saved=3, trainer=trainer, tag="test", save_handler=save_handler
)
```

Any other ideas @sdesrozis @erip ?


tests/ignite/contrib/engines/test_common.py::test_save_best_model_by_val_score tests/ignite/contrib/engines/test_common.py::test_gen_save_best_models_by_val_score tests/ignite/contrib/engines/test_common.py::test_add_early_stopping_by_val_score tests/ignite/contrib/engines/test_common.py::test_deprecated_setup_any_logging tests/ignite/contrib/engines/test_common.py::test__setup_logging_wrong_args tests/ignite/contrib/engines/test_common.py::test_setup_wandb_logging