Roma chief Walter Sabatini is hoping to secure the signing for new coach Rudi Garcia for the upcoming season, having been encouraged by the status both players hold at their clubs.
Nani's contract expires in 2014 and according to Corriere Dello Sport, there are no plans at United to renew his deal.
Nani recently spoke of his United future after having a turbulent season at the Premier League champions.
He said: "My future? Nothing is certain. I am calm. I have everything in my hands.
"I am not saying that I will not continue at Manchester United. I will think about what is best for me."