Iran's striker only moved to Inter a year ago, but assesses his situation after wrestling to get a regular start under former coach Simone Inzaghi.
Taremi was limited to a back-uprol for Senior Center-Forwards Lautaro Martinez and Marcus Thuram.
La Gazzetta Dello Sport says that Taremi is now considering his options, with Fulham and Besiktas in contact now.
No formal approach has been made, but the Taremi camp was made aware of the interest of both clubs.