The 36-year-old’s Ibrox deal expires this summer, but he has no plans to hang up his boots.
Instead, the Northern Ireland skipper is hoping to help lead Gers back into the group stages of Europe’s premier club competition for the first time in 11 years.
Davis was a UEFA Cup finalist with Walter Smith’s side back in 2008 and also a member of the last Gers squad to make it into the Champions League proper back in 2011.
And he would love another crack at the competition next term.
“Reaching the Champions League would be massive for everybody and the players are no different,” he said. “It’s the stage you want to play on and to get another taste of that at my age would be very nice.
“I don’t tend to look too far ahead. I feel good at the minute and as you can clearly see I’m enjoying my football. How could you not with the season we’ve had so far?
“So I don’t see myself finishing up at the end of the season.”
Gers boss Steven Gerrard has already made it clear he will wait until his side have wrapped up the title before opening talks on new contracts.
That could come as early as Sunday after the Light Blues closed to within four points of the title.
Victory over St Mirren on Saturday would leave Celtic having to beat Dundee United at Tannadice 24 hours later to avoid Gers being crowned champions with six games to spare.
Even if Celtic take maximum points, the Ibrox faithful would then face the dream scenario of their team going to Parkhead on March 21 with the chance to win their first league crown in a decade at the home of their bitter rivals.
Whenever it finally comes, Davis is in no rush to sit down and talk numbers.
He said: “My approach has been the same as the club’s – let’s concentrate on the football first and foremost and get ourselves into a position first.
“I’ve got a very open relationship with both the gaffer and Ross Wilson (the sporting director) at the club.
“We’re always talking about different scenarios, so I’m not under any pressure or worried about the situation moving forward.”
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