That's according to Monaco sporting director Vadim Vasilyev.
He claims the Premier League champions have proposed a deal, while also revealing the Ligue 1 club are still looking to add a few faces to their much-changed squad.
Nani suffered a turbulent season during the 2012-13 campaign, making just seven league starts.
"We still have time to make a few alterations before the end of the transfer window, if needed."
Nani was a firm favourite during the his first years at United, and has made 212 appearances while scoring 40 goals.