Yilmaz impressed for Besiktas last season, racking up 27 appearances in the league and registering three goals along with four assists.
His displays caught the attention of Rangers and they appear to be turning to him after selling Calvin Bassey to Ajax.
With Yilmaz’s contract expiring next year in summer, the Turkish giants were claimed to be open to selling him and now it appears Rangers have succeeded in their pursuit.
Rangers are claimed to have reached an agreement with Besiktas for the transfer of the left-back with the fee being €6.5m.
Further, the Turkish giants will also retain a sell-on clause where they will earn 20 per cent of any profit resulting from a subsequent sale.
While the two clubs have settled between themselves, Rangers are yet to reach a personal agreement with Yilmaz.
The left-back’s representatives have started discussions with Rangers over the terms of a contract and once that hurdle is overcome, Yilmaz will be in line to become a Gers player.