United were reported to be close to a £30million deal for the Portuguese international after the player’s representatives met with Moyes in January.
But Moyes’ Old Trafford departure last month looks to have halted a possible deal this summer, allowing Liverpool boss Brendan Rodgers to make his move.
The Anfield boss has admitted he wants to strengthen his title challenging side over the summer and will make tightening up his leaky defence a major priority.
And Carvalho’s defensive abilities have got Rodgers interested in completing a deal, and could help provide the protection Liverpool’s defence so evidently needed at times last season.
But Liverpool will have to break their transfer record – currently £35million for Andy Carroll – if they are to secure a deal for the 22-year-old, with his contract having a £37m release clause in his contract.