The Turkish giants are continuing to monitor Frei with their coach Fatih Terim naming the 19-year-old Austrian-born winger as a player of interest to the Istanbul club.
Frei came on as a substitute for Turkey against Denmark in midweek and looks set to commit his international future to his father’s country of birth, having played for Switzerland at Under-21 level.
Galatasaray could have been sensing a bargain when Frei was farmed out to Cardiff but injuries to Bryan Ruiz and Alex Kacaniklic could catapult him straight back into the Fulham side when his first month at the Cardiff City Stadium is up.
Frei joined Cardiff on October 26 and boss Martin Jol has revealed he can recall him after 28 days, which means the teenager could be back in the Cottagers squad for the Stoke City game on Saturday.
Bayern Munich have entered the race to Emre Can, who continues to talk up a move away from Liverpool this summer.