Costa has become Portugal's number one after ousting Rui Patricio from that spot shortly before the World Cup in Qatar.
Despite coming up short domestically and on the continent with Porto though, Costa looks set to earn himself a big move.
A Bola claim the highly-rated Porto stopper has a £65m clause in his deal at the Portuguese giants, and that United are willing to meet it to bring him to the Premier League.
That brings David de Gea's future into question, and the Daily Mail claim that the club are holding fire on signing off on his new contract despite an agreement being reached.
De Gea was presented with the Premier Golden Glove at Old Trafford when United faced Fulham, but the club now appear hesitant to keep the Spaniard with his contract up in the summer.
David Raya was another name being linked with a move to the Red Devils, but a deal for Costa may be more straightforward for the club given the release clause in his contract.