The Red Devils chief is set for a major summer of transfer action as he looks to rebuild his underperforming squad.
Central midfield is seen as an area of particular concern, with the likes of Marouane Fellaini, Tom Cleverley and Michael Carrick having failed to impress.
Moyes is believed to be looking to add a combative and energetic force to his ranks, and has outlined Carvalho as a top target.
The 21-year-old enforcer has been earning rave reviews for his performances in the Portuguese top flight, where he is regarded as one of the very best emerging players around.
United are said to have scouted him on numerous occasions, and are convinced that he can help to solve their current issues.
Carvalho currently earns less than £5,000-per-week, and Moyes is ready to hand him a major pay hike to move to Old Trafford.
Sporting are desperate to keep their man, but know that they cannot compete financially with United.
The starlet has been compared to former Arsenal icon Patrick Vieira due to his rangy playing style and physical presence.