Rangers have received an offer for captain James Tavernier from Turkish club Trabzonspor.
It is understood Rangers would consider selling the 32-year-old if his value is met as manager Philippe Clement rebuilds his squad this summer.
Süper Lig clubs have already signed former Ibrox players Borna Barisic and John Lundstram after their contracts expired.
Tavernier joined Rangers in 2015, scoring 125 goals and contributing 129 assists during his time at Ibrox to become the highest-scoring British defender of all time.
He has won a Scottish Premiership, Scottish Cup and League Cup title during his nine years at the club – and helped Rangers reach the Europa League final in 2022.
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A look back at some of Rangers captain James Tavernier’s best goals for the Gers in the Scottish Premiership
Former Gers bosses Steven Gerrard at Al-Ettifaq and Giovanni van Bronckhorst at Besiktas have also been linked with a move for their former captain.
Speaking during Rangers’ pre-season camp in the Netherlands, Clement revealed the club would consider bids for players except goalkeeper Jack Butland.
Rangers manager Philippe Clement (right) would consider bids for captain Tavernier
That could pave the way for the likes of vice-captain Connor Goldson, midfielder Todd Cantwell and striker Cyriel Dessers to also depart this summer if reported interest formalises.
He said: “If there’s somebody coming with the right amount of money we will see, we will discuss. But you always need to see, then you need to replace somebody, and you need enough money to replace them to make it better, otherwise it is also of no use. It’s finding a balance in that way.
“I believe there is only one player that is irreplaceable at the moment, that I don’t think a team will pay the money he is worth, for sure, and that is Jack Butland. Everybody knows what I think about that. Every player falls in to that category – Jack doesn’t.
“If somebody comes with £30-£40m you can replace him [Butland] for that money. If it is a good amount you can replace him and do something else. We will see.”
Rangers have signed seven players this summer in Hamza Igamane, Jefte, Clinton Nsiala, Liam Kelly, Connor Barron and Oscar Cortes – who rejoined on loan with an obligation to buy in the summer – while Mohamed Diomande made his loan move permanent.
When does the summer transfer window open and close?
The 2024 summer transfer window is now open and will close on August 30 at 11pm UK time in England and at 11.30pm in Scotland.
The Premier League and Scottish Premiership brought forward Deadline Day to link up with the other major leagues in Europe. The closing dates were set following discussions with the leagues in England, Germany, Italy, Spain and France.