Moyes, who is leaving Merseyside after over 11 years in charge to replace the retiring Sir Alex Ferguson at Manchester United, is happy to help chairman Bill Kenwright find a new boss.
And he says his backroom men of Alan Stubbs, David Weir and Duncan Ferguson - all former Everton players - are all excellent candidates.
"I would always recommend the people who are around me," Moyes said.
"A lot of them know how the workings of the building (at the training ground) are, how we move things forward and the restraints the club has, so it is easy for them to deal with that.
"We (Moyes and Kenwright) speak a couple of times on the phone, and if he has anything to say or wants me to help him, I will do so."
Moyes believes Kenwright will "get it right" when he appoints the new manager, adding: "I think continuity at every club is important.
"You can't always just have a complete clean slate and start again. But these are questions you need to wait to ask the chairman about when the time comes."
Kenwright vowed at Everton's end of season awards ceremony last night that Moyes' work at the club would not be allowed to go to waste, saying of the Scot: "When he came to me, when we first met on my sofa 11 years ago, he said, 'chairman, you're not going to go down.'
"Well, we didn't go down and he's kept us there (in the Premier League) and taken us forward.
"And although we will miss him like there's no tomorrow, I promise you David, we will maintain what you have started. I personally will not let you down."
Phil Neville - ruled out of the final match of the season at Chelsea - has also been linked with a role at Everton, though there has also been talk that Moyes is considering taking his captain to Manchester United with him.
Moyes said: "He is a great man. He is someone who has been a great player and is a great ambassador for the club.
"If Phil Neville could take a job up anywhere...he is really, really good at what he does, he is going through his coaching badges just now and he would be a good choice for any club."