The Spanish sports newspaper claim that Valdes has received an offer from the Yellow Canaries and that he is open to the transfer after being convinced by the ambition of the club.
The report also states that Valdes has had offers from reigning champions Galatasaray and Istanbul rivals Beşiktaş.
HaberTürk recently reported that Beşiktaş manager Şenol Güneş vetoed a move for Valdes opting to keep his faith in current keepers Tolga Zengin and Cenk Gönen.
The experienced keeper had been closely linked with the Black Eagles but Güneş reportedly does not want the club to pursue the Spanish international.
Valdes would become the third former United player at the Yellow Canaries should he join.
Turkish international keeper Volkan Demirel is currently first-choice keeper at Fenerbahçe but Valdes would be expected to replace him should he make the move.