As reported by the English outlet, United are keen on securing a deal for the Brazilian before the start of the World Cup, which begins on June 14. The midfielder is 25 years old, and has long been linked with a move to the Premier League.
United's rivals Manchester City were rumoured to be interested in him in January, however it is Jose Mourinho's side who look set to bring him in during the summer window.
'Sky Sports' sources claim that United are in advanced talks with Shakhtar Donetsk over a deal for Fred, who was recently named in Brazil's squad for Russia.
The midfielder has seven caps for his nation, and has contributed four goals and seven assists in all competitions for Shakhtar this season.