The 29-year-old has been a key player in the club’s title success.
Tavernier, despite missing the last seven matches, scored 17 goals in all competitions. In the Premiership he has scored and assisted 20 goals.
It is form which has led to reported interest across the past couple of seasons which could be reignited this summer.
The player, however, has been tipped to finish his career at Rangers by former England international Kevin Phillips with the lure of the Champions League likely to ensure he remains put next season.
“I think he might stay there for the rest of his career if he is happy there,” Phillips told Football Insider.
“He has just won the title, he is the captain, and he will be playing Champions League football next season.
“Yes, Premier League football is difficult to turn down but he is working under a manager that has been there, seen it, done it. Why would you want to leave?
“I am not surprised to hear that he’s happy there and I think he might sign a new deal and stay there for the rest of his career.”
Tavernier, who is contracted until 2022, is expected to return from injury in the coming weeks and will be one of the favourites to land player of the year gongs at the end of the season.
He will lift the trophy at Ibrox on May 15 when Rangers host Aberdeen on the final day of the season.