The Daily Star reports that United boss David Moyes is keen to continue the club's policy of developing youth players and could make a move for Goncalves as early as January.
"Signing Adnan Januzaj on a new five-year contract at Old Trafford shows the club's willingness to go out and try to sign the best players," Moyes wrote in his programme column for United Review.
"Young footballers get opportunities to progress here at Manchester United and I have no doubt that, in the future, Adnan will become a top player. He is 18 years old, has good ability, plus maturity beyond his years.
"All aspects of his game will continue to improve the more he plays matches but already he has made important contributions to the team through both making and scoring goals."
Moyes signed youngster Saidy Janko from Swiss side FC Zurich in September.