The report claims the Istanbul giants will pay the rest in instalments.
Nani is expected to sign for the Yellow Canaries after his agent Federico Pastorello reached an agreement with Fenerbahçe sporting director Giuliano Terraneo last week.
The Portuguese international is currently on holiday and is expected to complete his transfer after returning from summer break.
Nani would become the Yellow Canaries fourth signing of the transfer window.
Fenerbahçe signed Simon Kjaer on a €7 million move from Lille and Bursaspor duo Şener Özbayraklı as well as last seasons Süper Lig goal king Fernandao.
Nani spent last season on loan at Sporting Lisbon scoring 12 times and providing eight assists in all competitions for the Portuguese giants last season.
The 28-year-old winger still has another two years left on his contract with United but is expected to leave after falling out of favour with manager Louis van Gaal.