The Besiktas captain has reportedly reached an agreement with Lille to sign a two-year contract.
Yilmaz, 35, will replace another veteran forward, Loic Remy, if a deal is finalised.
Yilmaz is one of Turkey’s most prolific strikers ever and has scored 230 goals in 440 career appearances.
In the 2019-20 Turkish Süper Lig season, Yilmaz netted 13 goals in 25 games.
The well-travelled marksman has also starred for his country with 24 goals for Turkey during his career.