The 50-year-old Scot believes his successor at Goodison Park should not necessarily be plucked from the lower leagues like he was by Bill Kenwright 11 years ago
Moyes joined Everton 11 years ago after spending four years with Preston North End and the soon-to-be Manchester United manager believes it may be better for the club if his replacement was experienced.
Moyes' final game at Goodison on Sunday was marked with a strong Everton performance and a 2-0 win over West Ham and after the game, the 50-year-old Scot reflected on his tenure at the club and said he was willing to help in the hunt for his replacement.
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"The chairman took a gamble at that time, giving a young British manager an opportunity to work so he needs a lot of credit for that.
"I think the difference now is when I took over it was maybe a bit easier to bring in someone a little bit less experienced.
"Maybe now, where Everton are, that might not be quite the case but if he wants me help I'll help him with whatever he wants.
"I'll do everything I can to help him in what he chooses to do next."
Wigan manager Roberto Martinez is the bookmakers favourite for the job, particularly after his FA Cup heroics on Saturday, with Cardiff City manager Malky Mackay and Celtic's Neil Lennon the other favourites.
"Whoever comes in will enjoy it because they are a great bunch of players," Moyes added. "I will walk away from here saying Everton have become better.
"They will never be as good as they were in the 80s when they won things but I think if you look since the Premier League started how many top-10 finishes we have had it has improved."