So far, the transaction in the inter-bank money market is dominated by unsecured lending/borrowing (PUAB), and mostly in a very short term maturity. Around 60% of inter-bank transaction is overnight. There may be some short-term debt instrument in OTC (over the counter market), but I believe in a very small numbers and not actively traded amongst bank.
There is also perhaps, an interest rate swap (IRS) or overnight index swap (OIS) in OTC market, as there is sometime a quotation in Bloomberg or Reuters. But, it seems not quite regular and the transaction is supposed to be in a very small number. Thus, in general, money market is not yet considered to better serve banks’ portfolio management.