The daily Turkish newspaper Sabah claim that Fenerbahce are preparing to table a loan offer for the France international.
Remy has been linked with a move away from Chelsea after failing to secure a place in the Blue’s squad.
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.
Galatasaray have been on the hunt for a new striker since the summer transfer window and have previously been linked with Lokomotiv Moscow’s Oumar Niasse and Newcastle’s Papis Cisse.
Remy was not included in France’s squad which will compete at Euro 2016 this summer.