The 19-year-old, who joined from Swiss side Grasshopper in 2011, has struggled to make an impact at Craven Cottage.
Frei made just eight appearances last season, but Aysal has admitted that the Turkish giants are weighing up a move. Terim reiterated this and revealed that the club have been scouting the youngster for over a year.
"We are interested in Kerim Frei," Aysal told Lig TV.
Terim echoed Aysal's sentiments, saying: "We have been scouting Frei for over a year and remain interested."
Frei has scored just one goal in 33 appearances for Fulham.