The report states that the Yellow Canaries are currently in talks with United over a transfer fee.
The Yellow Canaries have submitted a bid worth €8 million for the Portuguese international.
Nani and Fenerbahçe are reported to have agreed on a four-year deal worth in the region of €4 million per-season according to the Sun.
The 28-year-old’s agent Federico Pastorello arrived in Istanbul last week and was spotted holding talks with Fenerbahçe sporting director Giuliano Terraneo.
The negotiations were successful according to NTV Spor and if an agreement is made with Manchester United Nani will become the Yellow Canaries second high profile signing of the season.
Fenerbahçe signed Denmark international Simon Kjaer from Ligue 1 outfit Lille on a €7.65 million transfer last week.
The 26-year-old defender joined the Istanbul giants on a four-year deal and became the most expensive centre-back to join the club.