The Everton boss is expected to be announced as the successor to Sir Alex Ferguson, who revealed on Wednesday morning that he is stepping down at the end of the season.
Sources have told Goal.com that the United players learned at the club's Carrington training ground Wednesday that Moyes is the man who has been lined up to take over from Sir Alex.
Everton has said that the club has not been approached by the new Premier League champions to negotiate Moyes' release but it is believed that the Scot will agree to a deal to take over at Old Trafford.
The 50-year-old will have to resign from his post at Goodison Park to complete the switch to United but he is out of contract at the end of the season and the process would be a swift, smooth and amicable one.
Moyes is a long-time friend of Sir Alex and the pair are set to enjoy a close relationship next season, given that Sir Alex is moving upstairs to join United's board of directors.
It is believed that Moyes has been personally cherry-picked by Sir Alex ahead of a number of Continental managers with proven European credentials.
The decision would then have been ratified by the United board, including the Glazer family, who own the club, and current chief executive David Gill, but they are believed to have been comfortable with Sir Alex having the biggest say in the identity of the man who takes his seat in the dugout.
A close circle of senior United figures have kept the plans shrouded in secrecy to avoid a repeat of the situation in 2001-02 when Sir Alex felt the team was unstable after he announced his intention to retire at the end of the campaign, only to later change his mind.
Moyes has established Everton as a top-six club during his 11-year reign on Merseyside despite having a budget that is dwarfed by his immediate rivals.
He has not won a trophy since moving to Goodison Park in March 2002 but United is putting greater store in his Premier League experience, motivational qualities, coaching nous and ability to get the most out of his players.
Everton is on course to finish above Merseyside rival Liverpool in the Premier League for the second consecutive season, a highly commendable achievement given the disparity in resources of the two clubs.
Gill, who will also leave Old Trafford this summer, has consistently said that United would seek an experienced candidate whenever the time came to make their first managerial appointment since November 1986.
Sir Alex held an emotional meeting with the players and senior coaching staff on Wednesday morning to tell them of his decision to step down as manager before he went to the main dining hall at Carrington to address a broader spectrum of club employees.
The indication given to staff is that Moyes is the man who will soon be announced as the new United boss.