The Aston Villa winger's representatives held talks with the Premier League champions earlier this month and personal terms were agreed before he jetted off on holiday.
He is now thought to have had a medical and is expected to finalise a five-year deal with United, who are hoping to make an announcement by the weekend.
The 25-year-old Young has just a year left on his contract at Villa Park and made it clear to the club he had no intention of extending that deal.
New Villa manager Alex McLeish admitted earlier this week Young was destined to depart this summer.
"It's not confirmed yet but it does seem likely," the Scot told talkSPORT.
"In my humble opinion it will be very difficult [to keep hold of him]."
Young's future has been the subject of intense speculation for some time, with a series of sparkling performances last season reportedly attracting the interest of several clubs.
As well as starring for England on several occasions, he continued to enhance his reputation with Villa during an impressive campaign.
Young's fine form could not help Villa finish higher than mid-table and he admitted at the end of the season that he wanted to play in the Champions League.
The 25-year-old now looks set to get his wish with Manchester United set to win the chase for his signature.
United have already secured the signing of Blackburn's England Under-21 defender Phil Jones for £16.5million and are likely to strengthen further with Atletico Madrid goalkeeper David de Gea the likely replacement for the retired Edwin van der Sar.
Young, like Jones, was also a target for Liverpool but United boss Sir Alex Ferguson appears to have once again beaten Kenny Dalglish to the player's signature.