The Glasgow giants have signed six players this summer and Giovanni van Bronckhorst is pushing the club to bring in more reinforcements.
The Rangers boss wants to add a left-back to his squad who could push Borna Barisic for a place in the team and Yilmaz is a player the Gers are targeting.
Rangers have been tracking the 21-year-old and are interested in taking him to Ibrox in the ongoing transfer window.
But it has been claimed that the two clubs are far away from reaching an agreement over a fee for Yilmaz.
For the moment, Rangers are not keen to pay the kind of money Turkish giants Besiktas are demanding for the left-back.
The Glasgow giants remain interested and will push for a move but for a deal to happen, Besiktas would have to lower their demands.
Van Bronckhorst wants defensive reinforcements and has added centre-backs Ben Davies and John Souttar to his squad this summer.
