Currency reserves are not the ledger. The ledger of the monetary system is, not surprisingly, the electronic ledger in the central bank that interconnect all the private banks.

The private banks have their own ledger, and, in that sense, they can create money. But if they have to operate outside their ledge, they need a "more real" money. That money, it's the ledger in the central bank (and cash).

This "more real money" is called "bank reserves" (not to confuse with reserves of gold or foreign currencies that are a different thing).