The Turkish sports newspaper report that sources from Portugal claim Nani will consider a move from Inter who are reported to be interested.
There has however, been no official confirmation from Inter, Fenerbahce or the players representatives regarding alleged interest.
Nani is also reported to be happy and well settled in Istanbul having established himself as a first-choice player under the stewardship of Vitor Pereira.
The experienced winger joined Fenerbahce on a £4.5 million transfer from United over the summer transfer window and has hit the ground running in Turkey.
Nani has 10 goals and eight assists in all competitions for the Istanbul giants this season.
The Portuguese international is currently rated the second best performing – statistically – player in the Turkish Super League according to Whoscored.