However, if reports are to be believed, the Premier League giants are considering an approach for Thiago Alcantara, who has just a year remaining on his Bayern Munich contract.
Despite the Spaniard being a first-team regular at the Allianz Arena, there have been several indications that Bayern do not want to risk losing the playmaker on a free transfer next summer.
Senior figures at the Bundesliga champions have also acknowledged that the 29-year-old is keen to experience a different league, a key factor in the strong speculation regarding a switch to the Premier League.
Although Liverpool are said to be the favourites for the former Barcelona's man signature, United may prove to be an attractive option if they qualify for next season's Champions League.
Here, Sports Mole predicts how United could line up if they have Thiago at their disposal.
While Pogba has linked up effectively with Bruno Fernandes in recent weeks, there would be question marks over where the arrival of Thiago would leave the World Cup winner in the pecking order.
With Fernandes a certain starter in a midfield three or as a number 10, Solskjaer would almost certainly use a defensive-minded player closer to the backline.
All things considered, Thiago will not commit to a transfer to Old Trafford unless he receives assurances over his spot in the team, which would likely see him take on a role where he links the defence and attack.
Although he has predominantly been deployed as a defensive midfielder this season, Solskjaer would prefer using a more physically-imposing player in that position.
If the Norwegian opted for a midfield three with less attacking intent, Thiago would arguably fit that system perfectly, having players either side of him to push further forward.
Nevertheless, everything points to Solskjaer putting together tactics which work in favour of star man Fernandes, something which may not necessarily help Thiago settle into life at a rapidly-improving team.