According to Italian media outlet CalcioMercato, the former Juventus star has been declared as surplus to requirement by coach Antonio Conte.
Owing to a knee injury and the arrival of Ashley Young from Manchester United during the last winter transfer window, Asamoah had searched for sufficient playing time at the Italian Series A giants.
The article goes on to say that the Turkish Super Lig giants Fenerbahce and Galatasaray all have made inquiries for the Liberty Professionals player but no talks are currently taking place.
Asamoah 31, made just 11 appearances across all competitions, in which he provided a single assist for Inter Milan last season.
The versatile player's current market value is €4,000,000.