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Although there has been no announcement from the club following on from Sir Alex Ferguson's retirement, Moyes is understood to be top of their list of candidates to replace the Scot.
It is impossible to see Moyes turning the offer down and as his contract with Everton is due to expire in the summer anyway, there is not thought to be any reason for the appointment to be delayed beyond the next 48 hours, with the potential for the process to be concluded as early as tomorrow.
It would see Moyes becoming United's 20th manager, and the seventh Scot, joining an illustrious list, which includes Sir Matt Busby, Tommy Docherty and, of course, Ferguson himself.
As rumours swept around Manchester last night of Ferguson's impending departure, it did seem there were only three plausible candidates, Moyes, Jose Mourinho and Borussia Dortmund coach Jurgen Klopp.
Given the short timescale United are working to, it was impossible to imagine Klopp resigning before Dortmund's Champions League final with Bayern Munich, whilst Sir Bobby Charlton, who has significant influence at Old Trafford, does not believe Mourinho's capacity for external and internal conflict sits well.
That leaves Moyes, even if his European experience, limited to just 26 games, which have yielded 14 wins, is less than United have managed in the last three seasons alone.
"The qualities we are looking for are the ones that have been inherent at Manchester United for many years," chief executive David Gill told MUTV.
"Our two most successful eras were with managers who got involved with all aspects of the club, from the youth team to the first team, and had that degree of loyalty and understanding of the football club.
"Clearly he has to have the requisite football experience, both in terms of domestic and European experience. It is a small pool but we will move forward."
Moyes' name is openly being discussed in the United dressing room and it now would be a sensational development if the 50-year-old was not installed, even if he could well end the season at Everton as Ferguson is not standing down until after his final game at West Brom on May 19.
Ferguson has never made any secret of his admiration for a fellow Glaswegian, stating as recently as February that a failure to secure a top-four berth was not a slight on Moyes.
"He's had 10 years at Everton - you don't survive 10 years in this game without making progress, that's obvious," said Ferguson.
"I don't think whether he gets in the top four changes mine, or anyone else's opinion of him."
Moyes will get his first taste of the difference between managing Everton and the job he is now set to undertake in July when he flies to Thailand for the start of United's pre-season tour.
It is not uncommon in the Far East for United staff to find fans waiting outside rooms, whilst it is almost obligatory for scores to camp outside hotels throughout any Red Devils stay.
Moyes' first official game in charge will be the Community Shield against either Manchester City or Wigan at Wembley on August 11, which could have become Ferguson's 50th trophy.
That statistic alone is enough to water the eyes of a man whose only silverware was the Second Division title he won at Preston in 2000.
With Ferguson remaining on the board, his shadow will hang over the club for a good while yet, whilst decisions on a backroom team who have shared in so much success over the years, and who know the intricacies of United so well, will be interesting.
Yet Gill is adamant the transition will be seamless.
"We knew this day would come," he said.
"We have been preparing for it. We have to look forward.
"The new manager will inherit a great squad and infrastructure off the pitch, with a great staff.
"The new person will be walking into a difficult situation in terms of the number of trophies, but the positive of also having the support of the Manchester United family.
"It is a dream job."