Carvalho has made 136 appearances for Sporting Lisbon since first playing for the Primeira Liga outfit back in 2011 but has been consistently linked with a move to the Premier League in recent seasons.
Arsenal are understood to be long-term admirers Carvalho but it appears Liverpool may now be the favorites to land the highly-rated 24-year-old midfielder.
A Bola suggest the Merseyside club are already in talks with Sporting director Bruno de Carvalho over a potential deal for the Portugal international.
However, the Reds may need to splash the cash in order to land Carvalho, with Sporting reportedly demanding a fee of around £26million for their prized possession.