The report states that the Lions are preparing to launch a bid for the France international during the January transfer window.
Galatasaray have been on the hunt for a new striker since the summer transfer window and have previously been linked with Oumar Niasse and Newcastle’s Papis Cisse.
The Istanbul based club’s first choice striker Burak Yilmaz has seven goals while his alternative Umut Bulut has only managed two goals in 16 games.
Remy has provided one assist and scored three goals in 12 appearances for Chelsea this season. The 28-year-old’s contract expires in July 2018.
Chelsea take on Sunderland this weekend in the Premier League. Galatasaray travel to Izmir to take on Akhisar Belediyespor in the next round of Turkish Super Lig games.