Fred fits the bill for United and could make the cut for Brazil's squad at the World Cup this summer.
According to the Daily Star, United have held discussions with Fred's representatives in recent weeks - making a big-money switch to Old Trafford all the more likely.
The former Internacional star arrived at the Ukrainian giants for €15 million in 2013 and has gone on to make nearly 100 league appearances for the club.
The summer transfer window is about to open and managers are working hard on their transfer targets so we'll bring you all the latest gossip from around the globe.
While admitting he is happy with his current situation, speaking recently to SporTV the 25-year-old Fred outlined a desire to progress. "I've been working well here but it has been five years".
Regarded by many observers as the key figure in a Shakhtar side that has just secured back-to-back Ukrainian Premier League and Cup doubles, Fred is keen to develop his career at one of western Europe's leading clubs. I have dreams of playing in major clubs in Europe.
Repoll in 568 booths tomorrow
All political parties, including civil society and judiciary, must play an active role to strengthen the democratic spirit". He said that it was a matter of grave concern and was against the concept of democracy.
"I think I have to change a little".
While a potential move to join compatriots Neymar and Marquinhos at Paris Saint-Germain has been touted as well.
Not only is Fred the type of midfielder Manchester United do not possess at the moment, but he is also Brazilian, which makes him all the more valuable for Mourinho, who previously admitted that he would love to add a Brazil worldwide to his squad.
Jose Mourinho wants to sign at least one central midfielder to replace the retiring Michael Carrick, with a second required should United fail to agree a new contract with Marouane Fellaini.
Who are Manchester United most likely to sign this summer?