The report states that Fenerbahçe have agreed personal terms with Nani and all that remains is for both clubs to agree on a transfer fee.
Nani’s agent Federico Pastorello has been in Istanbul holding talks with Fenerbahçe sporting director Giuliano Terraneo.
Fenerbahçe will offer €4 million per-season on a three-year deal according to the Sun.
Nani will find himself among Portuguese international teammates Raul Meireles and Bruno Alves if he joins the Yellow Canaries.
The club is also managed by Portuguese manager Vitor Pereira who took over on a two-year deal last week.
Nani’s childhood friend Manuel Fernandes is also well known at Turkey and was a fan favourite at rival Istanbul club Beşiktaş.
The Portuguese international is expected to leave United over the summer after falling out of favour with head coach Louis van Gaal.