The Yellow Canaries reportedly rejected an £8.4 million bid from the Black Cats as it falls below his valuation of the 29-year-old striker.
The Daily Star report that Fenerbahçe president Aziz Yıldırım wants at least £14 million for the experienced striker.
Sunderland could however, face competition from fellow Premier League club West Ham who also have their eye on the Senegalese international.
The Express report that the Hammers are preparing a £12 million bid for the 29-year-old striker. West Ham boss Slaven Bilic is familiar with Sow having coached the team of his Istanbul rivals Beşiktaş for two seasons.
Sow striker scored 16 goals and provided eight assists in all competitions last season and still has another year left on his contract.
The Senegal international won the Ligue 1 with Lille in 2011 and the Süper Lig at Fenerbahçe in 2014.