It's thought that Fred could be a replacement to Marouane Fellaini, with the Belgium worldwide becoming out of favour with Mourinho. Michael Carrick has retired and Marouane Fellaini may not sign a new contract, leaving Mourinho short of players in the middle of the park.
Fred has been linked with Manchester United since the January transfer window, while Manchester City, too, were believed to be keen on the midfielder, with reports of the Citizens making an offer for the 25-year old also surfacing.
Shakhtar Donetsk president Rinat Akhmetov has confirmed that his club are preparing to sell Fred, after they rejected a big offer for his services from Manchester City last summer.
So what would Fred bring to this Manchester United side?
Fred was a target for Manchester City but sources have told ESPN FC manager Pep Guardiola has moved on to other options including Napoli midfielder Jorginho.
Along with Daley Blind and Luke Shaw, Darmian has little future at the club as Mourinho, who signed a new contract in January that will keep him at Old Trafford until at least 2020, seeks reinforcements.
However, it now seems Manchester United have managed to pip the newly crowned Spanish champions for the signing of Fred.
The Brazil worldwide is linked with a move to United, with champions Manchester City having nearly landed the 25-year-old in January.
Fred played an important role in Shakhtar's title win in Ukraine this season.
City subsequently identified Fred as the ideal challenger to Fernandinho, who at the age of 33 may not have many years at the top of the game left in him.