The 29-year-old forward has been deemed as surplus to requirements at Stamford Bridge with incoming boss Antonio Conte keen to sign a new star striker.
The Mirror newspaper states that Fenerbahce are plotting a move for the France international.
The daily tabloid goes onto state that Fenerbahce failed to sign Remy with a loan bid back in January however, believe they will succeed with a permanent move now with Chelsea’s squad set to be revamped.
The 28-year-old who joined Chelsea in a £10.5m move from QPR last year, has struggled with injuries and a lack of form in recent months.
Remy provided one assist and scored three goals in 20 appearances for Chelsea this season. The former Marseille man has two years remaining on his contract with Chelsea.
The experinced striker was not included in France’s squad which will compete at Euro 2016 this summer.