Yilmaz, 21, was signed from Besiktas last summer but has found life tough in Scotland, having managed to feature in just four league games so far, the latest being Saturday’s 4-2 win at Motherwell.
Borna Barisic is the first choice left-back and it is claimed Rangers now do not even view Yilmaz as the man they want as backup.
According to Turkish outlet Fanatik, Rangers are not including Yilmaz in their plans for next term and are prepared to ship him out.
Besiktas are alive to the situation and are keen to bring Yilmaz back to Turkey on loan.
It is suggested that Rangers are open to letting the defender depart on a loan deal in the summer.
Whether Yilmaz can convince Rangers boss Michael Beale to change his mind in the coming weeks remains to be seen.
The 21-year-old, whose contract with the Glasgow giants runs until the summer of 2027, has six international appearances for Turkey.
A product of Besiktas’ youth academy, Yilmaz was considered a bright talent at the Turkish giants.