The report states that the 29-year-old wants out at Stamdord Bridge after failing to break into the starting eleven since joining in 2014.
The report goes onto state that contract negotiations are on going and that Galatasaray are looking to loan Remy until the end of the season.
The Turkish sports paper AMK report that Galatasaray have sent their general secretary Faith Isbecer to London in order to discuss the possibility of signing the striker.
The Istanbul Giants have been on the hunt for a new striker since the summer transfer window and have previously been linked with Oumar Niasse and Newcastle United’s Papis Cisse.
Galatasaray’s first choice striker Burak Yilmaz has seven goals while his alternative Umut Bulut has only managed two goals in 16 games.
Yilmaz has recently suffered a reoccurrence of a hamstring injury keeping him out until the end of January.