The Turkish newspaper AMK reports that Galatasaray’s general secretary Fatih İşbecer has held talks with Chelsea over the possibility of loaning the France international.
Remy has struggled with injuries and a lack of form in recent months and may opt for a move in order to secure his place in the French national team ahead of Euro 2016.
The 28-year-old joined Chelsea in a £10.5m move from QPR last year.
Remy has started only one Premier League game this season, scoring twice in the League Cup and once in the league.
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.
The Lion’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.