Football agents Federico Pasterello and Luca Bascherini arrived in Istanbul yesterday representing Nani and held talks with Fenerbahçe.
The agents met with Fenerbahçe sporting director Giuliano Terraneo and the negotiations were reported to have been successful.
Nani has also been linked with a move back to Portugal but recently ruled out a transfer to Benfica.
“No, I don’t think about possibly signing for Benfica and I don’t want to talk about it as I said before,” Nani was quoted as saying in the Daily Star.
Nani spent last season on loan at Portuguese giants Sporting Lisbon where he racked up 12 goals and eight assists in 38 appearances.
The Portuguese international still has three-years left on his current contract with Unıted and currently earns €140,000 a week.
Fenerbahçe could face competition from rivals Galatasaray who have also been linked with the 28-year-old in the past.
The Yellow Canaries finished last season as runners up and booked a place in the Champions League play-off round.