Some had expected Everton to go through a year of transition under Roberto Martinez, but Moyes’ successor has enjoyed a superb first year on Merseyside.
Everton are one point adrift of the top four and had it not been for a midweek defeat to Crystal Palace, Martinez’s team would have been in pole position to pip Arsenal to the final Champions League qualification place.
Moyes, on the other hand, has struggled during his first term at Old Trafford.
Moyes admits it is almost "mathematically impossible" to catch Everton or Arsenal, but he does not begrudge his old side any success.
"I’m looking forward to going back as I had some great times and worked with great people and, more importantly, some great players," Moyes added.
"They were terrific and I’m really pleased to see them doing well.
"Roberto has done a brilliant job there in the time he has been in charge.
"He’s got them playing well and in a good, healthy league position so I go back with some great feelings but I’m back now as Manchester United manager and my focus is on that now."
With United so far off the Champions League places, it is clear that Moyes needs to overhaul his squad if he is to challenge for a top-four finish next year, let alone the Premier League title.
The Scot has been linked with moves for Toni Kroos, Luke Shaw and a number of players from the Portuguese league, including William Carvalho, Eliaquim Mangala and Jackson Martinez.
Moyes says his attempts to bring in new players next year are progressing well, even though United are no longer able to offer Champions League football.
"I’m well into my planning with my thoughts and ideas getting ready for next year," he said. "We’re linked with player after player and, every time I go to a game, I’m supposed to signing three or four players from that game.
"That isn’t the case, but everyone is well aware we are looking to make signings and will try to do that whenever the opportunity arises.
"It will probably be after the end of the season before anything takes place but we have got to look to do one or two things."