The Premier League champions have been tracking the Portuguese international during the course of the season as they are said to be weighing up a potential move for Carvalho.
Manchester United boss David Moyes is said to have identified the 21-year-old as the man to bolster his midfield options, as he believes his side's engine room is an area that needs improving.
Earlier reports had suggested Manchester United had agreed to meet Carvalho’s £37million release clause, however Sporting Lisbon president Brune de Carvalho denied claims the midfielder is on the verge of leaving the Estádio José Alvalade.
The president did however say that he would not stop Carvalho from leaving the club if a club decided to stump up £37million for the box-to-box midfielder.
Carvalho is one of several players Manchester United are expected to sign in the summer as Moyes is planning a major overhaul of his struggling side.
Manchester United are said to have a good chance of beating the likes of Chelsea and Real Madrid to his signature as Carvalho is represented by Portuguese super agent Jorge Mendes, who has close links with the north-west side due to the fact that he represents Nani, David de Gea and former assistant manager Carlos Queiroz.