Nani signed a new five-year contract with Manchester United last September, but David Moyes has used him in just five Premier League starts this season.
Ashley Young has often been played instead of Nani.
"Nani is a very important player and at this time the only thing I can say is that he is likely to leave Manchester," agent Andrea Pastorello said to Violanews.com.
"The problem for Fiorentina and other Italian clubs is the player’s salary. But we will evaluate all bids.
"Our relationship with United is great. Fiorentina have to speak with Manchester United about Anderson [who is on loan from the Reds to the Florence club], and maybe there will be an opportunity to talk about Nani too."
Nani arrived to United on a transfer in 2007.