Moyes has left the club and will be replacing Sir Alex Ferguson at Old Trafford next season while Neville is taking time to consider his future following the end of his playing spell at Goodison Park, eight years after his arrival from Manchester United.
He will see a specialist about a knee problem before deciding on whether or not to continue playing but Moyes expects him to turn his hand to coaching.
“I think he’ll probably go into coaching or management, that would be my tip,” Moyes said.
“He has got a bit of problem with his knee, but he’ll know if he can play on or not.
“He’s a great man and has a lot of good values. I can see him being successful in the future.”
On whether Neville could be a success at Everton, who are now looking for a new manager after the end of Moyes’ 11-year reign, the Scot said: “He could [stay on]. He’s capable, he’s got good values, he knows the job and knows what’s expected. He could do that.”
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