The report states that Fenerbahce are open to offers from the Senegalese international and will consider bids close to their asking price.
The Turkish newspaper AMK claim that Sunderland have been closely linked with the 29-year-old striker and that the Black Cats are preparing a bid.
Sow – who joined Fenerbahce from Lille for €10 million in 2012 – has one year remaining on his current deal with the Istanbul giants.
The Fenerbahçe striker is expected to keep his place in the team should he stay as Nigerian international Emmanuel Emenike has been loaned out and Dirk Kuyt was signed by Feyenoord.
The 29-year-old striker has won two Super Lig titles and the Turkish Cup since signing for the Istanbul giants.
Sow provided eight assists and scored 16 goals in 40 appearances for Fenerbahce lasts season.