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Can bluetooth low energy master device go sleep when there is no communication to slave?

Generally , bluetooth low energy slave device can go sleeping after it established communication to the initiator (or the master).

Would it be possible to keep master sleeping after communication established as well?
If it's possible , how to maintain/synchronize communication between master and slave.
or Can this is already supported by TI software library?

Background

I 'm searching for the wireless ranging application which utilizes RSSI from wireless hardware engine.
(There could be many ways implementing this but using bluetooth would open way connecting to smartphone).

There will only be 2 devices in the loop ,asking for each other's range via RSSI value.
The distance does not need to be precise , application is only for simple tracking.