The 31-year-old is on the cusp of ending his stay at the Nerazzurri after a frustrating spell due to recurrent injuries.
Asamoah's troublesome knee has cost him his place in the UEFA Europa League campaign, forcing him to look elsewhere.
With Inter almost always doing double sessions, Asamoah's knee appear not to be able to deal with the robust training.
Remaining in Serie A will be very difficult for Asamoah unless he is to drop his wage demands.
He currently earns €3 million a year, a sum which prohibits many Serie A teams from moving for him.
The report goes on to explain that Turkish Super Lig giants Fenerbahce and Galatasaray have both made enquiries for the former Juventus player but there are currently no negotiations taking place.
Last season Asamoah made just 11 appearances across all competitions, in which he provided a single assist for his teammates.