The Daily Express says that the teenager has completed his medical and agreed personal terms, and an official announcement will be made in the next 48 hours with United "ready to pay nearly £20m" for his services.
United need to bolster their squad if they are to renew their challenge against cross-city rivals Manchester City, who they trailed by 19 points in last season's Premier League.
However, he is far more of a creator than goalscorer as his record of just 15 goals in five years at Shakhtar suggests.
Firmino has revealed he passed on his best wishes to Fred but warned that national allegiances will be put to one side when Liverpool face United next season.
Lions, tigers, jaguar escape German zoo
Eifel Zoo has nearly 400 animals of 60 exotic and native species, including lions, tigers, and other big cats on its 30-acre site. The Eifel zoo, owned by the Wallpott family, is home to around 400 animals, also including a Siberian tiger.
Midfielder Fred also got his black barnet newly coiffured and shaped, with a special gel added that made his spiky curls glitter.
Fred will hope to make the same impact on the Premier League as Brazilian global team-mates Willian and Fernandinho, who also arrived in England via spells with Shakhtar. However, FIFA extended the punishment to a worldwide ban in 2016 which ruled him out for four months.
"He is excited to start but now is the time to think about the World Cup".
"Players are always thinking of their careers".
Rivaldo is also familiar with Jose Mourinho's methods from their time together at Barcelona, and he said of Fred: "He is a wonderful player".