The Red Devils have been heavily linked with a move for the Brazilian in recent months, and are understood to have been in pole position for his signature since Manchester City dropped out of the race in January.
However, Metro reports that Fred is stalling over a decision amid speculation that Paris Saint-Germain could attempt to hijack the bid.
The 25-year-old could be attracted to linking up with the Brazilian contingent at PSG, and has previously suggested that he will wait until after the World Cup before making a final decision over his future.
United are keen to push the transfer through before this summer's tournament in Russia, though, and have made it clear to Fred that they are not prepared to wait for him.
Fred, who has a release clause of £53m in his contract, scored four goals and created seven more in 37 appearances for Shakhtar this season.