The report claims that Ronald Koeman is keen on bringing in the former Fulham youngster but that Besiktas want at least €7 million for the Turkish international.
The Istanbul giants are keen on keeping hold of Frei who is expected to enjoy an important role in the team with Gokhan Tore on loan at West Ham.
Frei did attract interest from West Ham last January when head coach Bilic confirmed interest in the 22-year-old according to the Fanatik.
The report quotes Bilic as saying: “Kerim Frei already has Premier League experience he is a player just about every manager could do with.”
The Mirror meanwhile claimed that West Brom were also plotting a move for the winger.
Frei is of course no stranger to top-flight football in England as he rose through the ranks of the Fulham academy before his move to Turkey two years ago.
The Turkish international winger started to break into the Besiktas first team team last season scoring five times and providing another five assists in all competitions for the Turkish champions.