The Dutchman has been a free agent ever since being released by Los Blancos, and the Turkish champions are supposedly ready to offer him the chance to relaunch his careerhere.
Galatasaray are interested in signing former Real Madrid man Royston Drenthe, according to reports in Milliyet.
The Super Lig champions are looking to add some more depth to their squad this summer, and they see the versatile Drenthe as a useful addition.
The Dutchman was released on a free transfer by Madrid at the end of last season, and he has since been looking for a new club.
The left-footed midfielder spent the 2011-12 campaign on loan at Everton, but the Premier League side opted not to sign him on a permanent basis after some inconsistent performances and rumoured off-field problems.
The 25-year-old seemed to have a bright future ahead of him after excelling at the Under-21 European Championship in 2007, but he has failed to live up to the high expectations since leaving his boyhood club Feyenoord.