The Red Devils were heavily alligned with the 22-year-old enforcer towards the back end of last season, with some outlets speculating that concrete approaches had been made.
But in recent months links between the Portuguese youngster – who has been on international duty at the World Cup – and United have cooled, with Chelsea thought to have taken pole position in the battle for his signature.
However Louis van Gaal is understood to be ready to partner Carvalho with fresh arrival Ander Herrera in a new look Old Trafford midfield.
Sporting are thought to be demanding around £24m for the latest starlet to emerge from their youth academy – which also produced Cristiano Ronaldo.
United are believed to be reluctant to meet such a fee, but given the numerous negotiations between the two sides in the past there is a chance that a compromise may well be reached.
Van Gaal is also said to be targeting Holland stars such as Bruno Martins Indi, Daryl Janmaat and Stefan de Vrij as he looks to overhaul his backline.