Moyes has one year to run on his current contract and as yet has failed to agree to a new deal.
Neville says it is imperative the Scot stays on Merseyside, saying it would be a 'massive disaster' if he left.
"The manager is the focal point of the club," Neville told Sky Sports News. "He is the one who has helped the club progress, he plays a large part in getting players in and keeping players happy, that is why we play so well, he motivates us and trains us well every day.
"It is so important the continuity continues with David Moyes as manager because you look at successful teams they have all had managers that have stayed there a long time and that has been the recipe of success at Everton in the last ten years.
"The whole club has been shaped by David Moyes so it would be a massive, massive disaster for him to leave, but I am sure that is not going to happen, I am sure he will be here for years to come."
"I think we cannot afford players to leave really because of the small squad we have got," added Neville.
"We are the fifth best team in England at the moment, it is difficult to think clubs below us would be buying our players.
"We want AJ to stay; the fans obviously want AJ to stay.
"He is loved around the place so hopefully he will stay and we can build on the success he has had at the club so far."