The Serie A outfit have long been linked with a move for the Portuguese international, whose contract at Old Trafford is due to expire next summer.
When asked about his client's future with the Premier League champions, agent Jorge Mendes refused to rule out the possibility of the 26-year-old moving on.
"Nani is a good player – the whole world knows it," Mendes told Radio Mana. "Will he go to Roma? Why not?
"Serie A is one of the best leagues in the world and Rome is a beautiful city. There is the possibility that he will leave United, but at the minute nothing is concrete. We will meet Manchester United and see, but there is interest."
Nani joined the Red Devils in 2007 from Sporting Lisbon.