Moyes to offer veteran duo new deals
The pair have played important roles in the club's encouraging start to the Premier League season and, although they are 34 and 35 years old respectively, the Scot believes that they still have much to offer at Goodison Park.
Both players' current deals are set to expire at the end of the season.
"We are monitoring Phil's position but, if you were asking me, I'd say: 'Let's give him another year's contract and keep it going'," Moyes told the Liverpool Echo.
"I'd say the same for Sylvain Distin, who is in the same position.
"With all due respect, when you get to their age, they understand most things are on one-year deals or rolling contracts.
"Both of them have been excellent and I'd have no qualms recommending to the board that we give them another year's contract.
"Phil and Sylvain are both in the same boat. I've not really sat and had a word with the chairman yet - we'll probably do that after the new year and see if we are ready to give them a new contract."
Club captain Neville is currently taking his coaching badges in preparation for the conclusion of his playing days but the former England international insists that he is not ready to retire just yet.
"I want to keep playing for as long as I can - at least one more year at the top level if I can," he said.
"I still have ambitions. For instance, I've always wanted to sample playing abroad, a different culture and different life experience for all the family.
"Time's running out, I know, and if the gaffer comes to me in January and wants me to stay another year then the decision's made for me."