The Turkish left-back moved to Ibrox in 2022 but could now be set for a return to his former club after an injury-hit three years in Glasgow.
Besiktas president Serdal Adalı said: “We’ve spoken with Ridvan Yılmaz.
“Nothing has been finalised.
“We’re talking to his agent and his club.”
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Yilmaz has often been linked with a move back to Turkey, including to Besiktas as well as Galatasaray.
However, he could be set to leave Rangers on a permanent basis after a lack of game time under new manager Russell Martin.
The left-back has not featured under Martin and has been replaced by new signing Max Aarons.
Aarons, traditionally a right-back, has been favoured on the left in recent matches.
Martin said last week: “With Ridvan, we’ve had an honest conversation and he’s sizing up his options, there are a couple of clubs interested in him so we’ll wait and see what happens.”
Besiktas are now in talks with Yilmaz and his representatives about a permanent switch.