The current deals of captain Neville, 36 in January, and Distin, 35 in a month, are due to expire in the summer.
But Moyes is keen to retain their experience and expects discussions to begin in January.
"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," the Scot 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."
- Sylvain Distin