The Shakhtar Donetsk midfielder has been heavily linked with a move to the Red Devils in recent weeks.
United lead their arch-rivals Manchester City in the race to sign the Brazil international, 25, this summer.
And according to The Sun, Fred will complete his move to United in the coming days.
They say the midfield maestro will arrive in the coming week, with the deal costing around £52.5m.
Brazil star Fred has reportedly been in talks with United since January – after a move to City fell through.
Fred has been vocal on his future in recent weeks, with the Shakhtar ace revealing both Manchester clubs want him.
“There was a possible transfer to City. Shortly after, both clubs – City and United – talked with Shakhtar and with my agents about a possible transfer,” he said.
“If I am not mistaken, there was news on Thursday of a strong bid by United.
“It’s an honour to be on the radar of great European coaches.
“I have a versatility on the pitch and I’m a multi-skilled player able to play in both midfield positions. I believe some coaches need that with their teams.
“I am focused solely on the World Cup. My agents are taking care of this.”
Jose Mourinho is well known for wrapping up his transfer business early and the Special One is said to be keen to get the Fred deal over the line as soon as possible.