The Yellow Canaries are keen to keep hold of Sow following interest from abroad.
The report goes onto states that Fenerbahce have been in talks with Sow and that a four-year deal has been agreed in principle.
AMK claim that Sunderland have been closely linked with the 29-year-old striker and that the Black Cats are preparing a bid. However, Fenerbahçe are understood to be holding out for €15 million for the Senegalese international.
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.