The Turkish giants are reportedly preparing a bid this week for Ayew, who was Villa's top scorer last season.
Aston Villa were always likely to have to field interest for several of their stand-out players this summer after their relegation, and according to Fotospor, via talkSPORT, one of those stars is Jordan Ayew.
Ayew was Villa's top scorer last term after joining from Ligue 1 strugglers Lorient a year ago, netting seven times in the Premier League after signing for a reported fee of around £8 million.
Not only did he find the net more than any of his teammates, but the 24-year-old forward was arguably the club's brightest spark in attack throughout the campaign, often looking a cut above the rest of the side.
It is no surprise, then, that Fotospor report that Champions League competitors Galatasaray are one of several clubs interested in signing the Ghanaian.
The report claims that the Turkish giants are preparing a bid which could be submitted this week to leave both Ayew and Villa with a big decision to make.
Villa are sure to be keen to hang on to one of their most impressive performers, and with the forward having signed a five-year deal only 12 months ago the ball could be in their court.
However, Ayew may make an official transfer request if he wants to force the move through, and talkSPORT, who cite the initial report, claim that the Championship side would consider letting him go if an offer comes in of around £9 million.
The pull of Champions League football is likely to appeal greatly to Ayew, who may well feel that he showed enough last season in a desperately poor Villa side to prove that he is too good to follow the club down into the Championship.