On Wednesday December 4, however, the Scot will welcome his former team to the Theatre of Dreams for the very first time, keen to extend United's unbeaten run to 13.
His successor at Goodison Park, Roberto Martinez, has hit the ground running since taking charge and has been performing minor miracles on Merseyside with Everton currently fifth yet arguably in direct competition with Arsenal for the honour of producing the most attractive football in the league.
By comparison, United sit in eighth and have struggled to string together a consistent thread of convincing performances, especially when transitioning between the league and Europe, where Moyes' team have so far enjoyed their most emphatic displays this season.
Wayne Rooney and co. head into their home showdown with the Toffees following a 2-2 draw away to Tottenham Hotspur which itself was preceded by a stunning 5-0 demolition of Bayer Leverkusen in Germany.
Meanwhile, Everton head to Manchester in red hot form having smashed Stoke City 4-0 at the weekend.
Can Moyes launch the home side up the table by making a statement against his old club?
Much will come down, as ever, to his team selection, so why not hit the button below to start up the slideshow preview on how United could line-up against Everton.
Robin van Persie remains a doubt due to groin and toe problems but could start on the bench.
Michael Carrick is likely to need a little while longer before he can have any involvement in the matchday squads whatsoever, and his absence will feel even keener without Phil Jones deputising in midfield.
The versatile Englishman picked up a yellow card against Spurs which triggered an automatic one game ban due to cumulative total of cards he has so far received this season.
Everton will also be missing some vital players with star man Leighton Baines out with a toe injury while Arouna Kone and former United midfielder Darron Gibson are both sidelined due to knee complaints.
While the last two years of Moyes' reign at Everton brought about some highly credible and eye-catching football, Martinez's team have arguably already overcome the standards set by his predecessor.
Romelu Lukaku, Gareth Barry and—based on his performance against Stoke—Gerard Deulofeu have all been brought in on loan from Chelsea, Manchester City and Barcelona respectively and have added plenty of quality to the squad.
Keeping Lukaku quiet and ensuring Everton's technically impressive midfield is smothered will be vital, although the impetuous nature of Ross Barkley could mean that even Moyes' best laid plans could be wrecked by a moment of genius by the teenager.
As mentioned in the previous slide, however, Baines will be absent with Bryan Oviedo deputising for the left-back while Seamus Coleman (pictured) is set to raid the right flank in support of James McCarthy and co.
Martinez has stressed to his players that the true obstacle for them to overcome in order to reach the Champions League exists in their minds, with The Guardian's Andy Hunter reporting that the Spaniard is determined to break the Toffees out of their "damage limitation" mindset.
Expect to see an ambitious Everton take to the stage full of confidence and eager to impress their hosts.
Given just how stylish and sophisticated Martinez's team have looked so far this season, under the mid-week floodlights this clash may yet feel like another famous European night at Old Trafford even if it's a decidedly Premier League focused fixture.
Goalkeeper: David De Gea
Anders Lindegaard hasn't got a chance of usurping United's No. 1, and fans will be hoping the former Atletico Madrid prodigy's presence in goal will be assured for many years to come.
Keeping in with the theme of the recent festivities, De Gea looks to be the only man with a realistic chance of overtaking Ryan Giggs' appearance record for the club.
Central defence: Nemanja Vidic (or Rio Ferdinand), Jonny Evans
Vidic was impressive against Tottenham at the weekend, and with Evans more than capable of acting as the more mobile defender in United's central partnership, their combination could get another run out against Everton.
Yet with another Premier League game against Newcastle United looming on the horizon for the weekend ahead, Moyes may decide to rest the Serbian and switch in Ferdinand to keep both veterans fresh.
Having last featured in United's 5-0 win over Leverkusen, the Englishman is also in good form, although Vidic's more physical approach may be better suited to handling Lukaku.
Either way, it appears that Evans may have reclaimed the role he secured for himself last season as the side's first choice central defender with his partners selected to graft onto his well-rounded array of skills depending on the opposition.
Full-backs: Patrice Evra, Chris Smalling
Out wide, Evra looks set to start due to a lack of other options although he will need support from his colleague on the left in attack judging by the isolation he suffered at times against Tottenham.
With Moyes treating Rafael rather cautiously and easing him back into action, Smalling looks likely to remain at right-back, which may also be the best option anyway considering the aerial presence of Lukaku and Nikica Jelavic.
Central midfield: Tom Cleverley, Marouane Fellaini
Moyes may not be the only United figure facing down their old club when Everton come to town.
Having been absent from the first team since United's 2-2 away draw with Cardiff City, Fellaini looks set to return to action following the suspension of Jones.
That means that Cleverley is likely to remain in the team too, with Ryan Giggs admitting himself that he needs Jones to do his running for him these days when speaking to ITV after his exceptional display against Leverkusen last week.
A partnership of Cleverley and Fellaini may not sound too appetising but it could work, with the Englishman's mobility allowing him to sweep up any stragglers left in Fellaini's wake.
The Belgian will hopefully be allowed to get on with doing what he does best—bullying opponents, breaking up play and disrupting Everton's rhythm—while his lither colleague deals with the creative side of things.
Attacking midfield: Nani, Shinji Kagawa, Antonio Valencia
With van Persie unlikely to play a part in the game besides a late cameo from the bench, it looks as though Moyes will start with a one striker formation, offering his roster of wingers and attacking midfielders an opportunity to impress at home.
Nani was in man-of-the-match form against Leverkusen and could be handed another start on the left against Everton, especially considering Danny Welbeck's lack of match fitness.
Assuming Valencia remains as the team's permanent fixture on the right wing—Wilfried Zaha played in an U-21 game against Blackburn Rovers earlier in the week and so looks unlikely to be involved—Kagawa will set up shop in the hole.
The Japanese still isn't as decisive as some fans would like, but he is growing in confidence and stature when played in the middle, with his lack of goals and assists failing to highlight the positive effect he has on the team's build-up play and passing poise in attack.
A landmark performance from the playmaker against Moyes former club would surely quash any objections held over the former Dortmund star by his new manager.
Don't be surprised to see Adnan Januzaj selected as an alternative option instead of Nani or Kagawa to add a blast of youthful exuberance to the mix.
Up front: Wayne Rooney
The former Everton prodigy has been United's player of the season so far with 10 goals and eight assists in 16 games.
Backed up by the balanced and varied attacking midfield line of Nani's trickery, Kagawa's smarts and Valencia's width—not to mention Evra on the overlap too—he will be ready and willing to make the most of the service available to him.
Below is how United could line up against Everton in the Premier League on Wednesday December 4.
GK: De Gea
DF: Smalling, Vidic (or Ferdinand), Evans, Evra
CM: Cleverley, Fellaini
AM: Valencia, Kagawa, Nani
Both teams head into this fixture with good records and strong recent results.
Should Martinez find a way to allow Everton to overcome their inferiority complex they could take advantage of United's second-choice midfield in a similar manner to how West Bromwich Albion and Southampton found joy against Moyes' men.
Rooney remains in fine fettle, however, and should his teammates and the manager's system perform as required, the former Everton striker could come back to haunt his former club once more.
Prediction: Another 2-2 draw—United's third in a row in the league!