The 27-year-old is out of action for a couple more weeks with a hamstring injury, but that has not put Inter off completing the deal before Friday’s deadline.
They have enquired about the possibility of a loan move with a view to a permanent deal, and may try and tempt United into doing business by offering former midfield target Fredy Gaurin.
However David Moyes has so far snubbed offers to take the Colombian midfielder, and is likely to do so again.
Nani is willing to leave Old Trafford, after struggling for first team football under Moyes.
The winger has made 226 appearances for the Premier League champions since signing from Sporting Lisbon in 2007, and has scored 41 goals.
Reports in Italy have also suggested Juventus are keen to sign the Portuguese winger, who is looking for a move that will offer him first team football ahead of the summer’s World Cup.
The signing of Juan Mata is likely to restrict Nani’s first team opportunities further, while United are also thought to be planning a move for another attacking midfielder in the form of Bayern Munich’s Toni Kroos, before Friday’s deadline.