Moyes spent 11 years in charge at Everton before joining United last summer.
"The Everton fans were always terrific in my time there - very supportive and always right behind the team. We go there with a great away record and go there trying to keep that going.
"I know the players at Everton - they are a great group of lads and great professionals who got on with the job and were self-motivated. Over the years, we continued to add players there and it was a great group of young players. The senior group there is very important too.
"Roberto Martinez has done a brilliant job this year. He's got them playing well and in a good, healthy league position."
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