The Portuguese starlet is thought of as one of European football’s finest emerging players, and has been heavily linked with Arsenal in recent months.
However, United are also in the race and are keen to beat their domestic rivals to the 21-year-old.
David Moyes is said to have grown frustrated with Nani, who has been a peripheral figure at Old Trafford for some time.
With the wide-man having signed for the Premier League champions from the Lisbon outfit in 2007, the Scot is hopeful that Sporting will be keen to accept him as a part of a deal for Carvalho.
Nani is believed to have no future at the club, and could be open to a switch back to his homeland in a bid to get his career back on track.
Despite an urgent need for signings, Moyes is willing to wait until the summer to strike a deal, with Sporting said to be desperate to keep the young talent until at least the end of the season.