Loopback interface in my environment. Should it be assigned its own subnet?

My hardening process is asking to set an IP on my loopback interface. We currently aren't using routing protocols. Everything is statically assigned.

I need to bind the loopback as an AAA source interface, NTP and ip tftp source interface.

Our management VLAN is 10, 192.168.10.250. Our NCM is using 10.1.1.162 and uses TFTP. NTP server is on 192.168.20.66.

Will any privately assigned IP work in this instance or should it be in tune with the MGMT VLAN subnet(192.168.10.X)?