The Turkish Super Lig broadcaster claim that both Italian clubs are interested but that Fenerbahçe are still in pole position to complete the transfer of the Portuguese international.
The report goes on to state that United and Fenerbahçe have reached an agreement over a €6 million transfer fee for Nani.
The Portuguese international is expected to part ways with United this summer despite having two years left on his contract.
The Yellow Canaries are reported to have agreed terms with the players agent after he flew to Turkey to hold direct talks with club sporting director Giulliani Terraneo.
The Istanbul giants have been busy in the transfer market and signed last seasons Super Lig goal king Fernandao on a four-year deal today.
Fenerbahçe also recently completed the transfer of Şener Özbayraklı and Lille defender Simon Kjaer on a four year contract.