Giovanni van Bronckhorst is also in discussion with Alfredo Morelos and Ryan Kent but the club captain, a Mark Warburton signing in summer 2015, is in talks to extend his stay and potentially trigger a rarity in modern football – a testimonial for a decade of service.
Tavernier insists he is settled in Glasgow for the foreseeable future and fully focused on leading Rangers into the new cinch Premiership season at Livingston this lunchtime before the Champions League qualifier against Union Saint-Gilloise on Tuesday.
"I don’t see myself moving anytime soon,” he said. “I’m really happy here, my family is really happy, my kids are happy. I’m always repaying Rangers for giving me my chance.
"The club gave me the foundation to go out and do what I love to do – play football. I can play with a smile every single week. As long as the club is pushing itself, and I’m pushing myself, I’m in a really happy place,” he said.
“A testimonial though would be an unbelievable achievement. You don’t really see ten years at a club these days. It would be a nice touch if it was to happen here,” Tavernier admitted. “It’s a special place, always competing for trophies and playing in the biggest competitions.
“Obviously that’s our aim this season – to get into one of the biggest, the Champions League. It’d be another box ticked. We know there is a lot of work to do, but that’s our aim.”
That is the lure van Bronckhorst also hopes can entice Morelos and Kent to sign on for longer with each player now inside the final year of their present deals.
“Both are important players loved by everyone inside the club and the fans, they are more than open to extend,” the manager said. “The taste in Europe will help and we are pushing for Champions League this season, which will help and hopefully they will sign.”