The 22-year-old is enjoying a very impressive season with Sporting in Portugal.
Goncalves has 15 goals in 22 games, and has a release clause for roughly £51.7 million.
United would prefer to sign the latter, but may find he is out of their price range, as other areas of the team also require investment.
Goncalves has played in a central role this season but is more than capable of playing on either wing.
Liverpool were linked with Goncalves last month as they search for another midfielder.