The 26-year old has 12 months to run on his deal at Ibrox and McCoist is keen for him to follow in the footsteps as goalkeeper Allan McGregor and wingback Steven Whittaker who this week signed long-term contracts.
"Hopefully Steven Davis will follow Allan and Steven,” he told Rangers TV.
"I don't want to tempt fate but contract negotiations are continuing with Steven and his representatives and I would be very hopeful that we could get something organised with Steven as well.
"He certainly comes into the same category as Allan and Steven. He has been a top player for us and instrumental in the spine of the side.”