The Red Devils were in talks with the Portuguese earlier and are believed to have had scouts during 0-0 weekend draw against Academica in order to assess his caliber.
Man United manager David Moyes has have limited funds to spend on the next transfer window following a club record £37m signature of Juan Mata from Chelsea.
Moyes is keen to bolster his defensive midfield option at the end of the season and the midfielder seems to be an ideal option to bring at Old Trafford.
The 21-year-old starlet has been in sensational form this season and with his impressive displays he is considered to be a shining star in Lisbon.
However, Carvalho’s contract with the club is running until 2018 with a tag of £37m release clause to his contract.