The Turkish Super Lig club are understood to be keen on taking the Frenchman to Istanbul on loan for the rest of this season, the report says.
Rémy, 28, has struggled to get regular first-team football at Stamford Bridge despite the club's troubles in front of goal.
A report in Sabah, the Turkish website, claims Galatasaray are ready to bolster their frontline and says Rémy is the man they want.
