The Toffees will be bracing themselves for a number of bids across the summer. Former boss Moyes could try to lure Goodison Park's biggest stars to Old Trafford, but which transfers are likely to take place?
Let's take a look at four links and whether or not they should go ahead.
Ah, the Leighton Baines link once more.
With the summer transfer window approaching, Manchester United's reported long-term interest in the Everton left-back is set to dominate many back pages, especially with Moyes installed as the Red Devils' new manager.
Everton are likely to resist any approach for the defender. Despite United's continued link with the Englishman, one has to ask whether his proposed move is going the same way as that of Wesley Sneijder.
Patrice Evra had a decent season for United. His performances improved, and at 32 years old, he has Alexander Buttner for cover. Although the Dutchman isn't a top class player, he showed signs of quality with every performance during his debut campaign.
Do United really want to spend around £20 million on a 28-year-old defender? Like Sneijder, I think Baines has missed his best opportunity to join the club, which would have been around two years ago.
Will Baines follow Moyes to Manchester United? No.
Marouane Fellaini's link to Manchester United makes perfect sense.
The Premier League champions need a combative midfielder that can impose himself on others. With Anderson considered for the chopping block and Paul Scholes retiring, United certainly need to bolster numbers in the middle.
Moyes has an excellent relationship with the Belgian midfielder. As discussed by B/R's Dan Talintyre, the 25-year-old appears to idolise Moyes as his father figure of football.
Fellaini is ready to make his Champions League debut and needs to regularly test himself against the best players in the world. A potential move would certainly be a natural one for all involved, as the afro-haired destroyer's abilities could become pivotal to the way Moyes' United builds upon the foundations left by Sir Alex Ferguson.
Will Fellaini follow Moyes to Manchester United? Yes.
Manchester United's defensive frailties threatened to define their 2012-13 Premier League season, but Ferguson's side managed to tighten things up after Christmas.
David Moyes' Everton conceded less goals than the champions last term. The Scot prides himself on a solid defensive line and has been linked with a £10 million deal for Phil Jagielka. Although the move seems plausible, there are a number of factors blocking such a transfer taking place.
Phil Neville's move away from Everton has outlined Jagielka as the new club captain. The 30-year-old is one of the squad's most experienced players and has a huge role to play now that Moyes has exited the club. Bill Kenwright would undoubtedly not want to lose another important figure from Goodison Park.
It's also worth noting that Jagielka's Everton contract doesn't run out until 2017. Manchester United would be gutsy to splash money on a centre-back who is likely to slow down in the next couple of years, especially as Rio Ferdinand and Nemanja Vidic already offer the Old Trafford youngsters plenty of experience to play alongside.
Will Jagielka follow Moyes to Manchester United? No.
First linked with Manchester United in 2011, the career of Ross Barkley hasn't progressed too spectacularly across the last two years.
Numerous injuries and poor form forced Moyes to send the player out on loan to Sheffield Wednesday and Leeds United. He also warned against immediate expectation, suggesting that the 19-year-old has a long way to go before he can regularly compete at the top level.
The England U21 international performed well across a handful of Premier League outings towards the end of the 2012-13 season, including the Old Trafford encounter against United. Although his original price tag of £30 million has depleted, Everton will still look for around £13.5 million for the prospect.
While Barkley could emerge to become a ready-made Manchester United player, he needs more experience with Everton before any deal can take place.
Will Barkley follow Moyes to Manchester United? No, not yet.
Which Everton players do you think will join Moyes at the Theatre of Dreams? Let me know in the comment section and be sure to follow me on Twitter right here:
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