Distin, 34, and 35-year-old club captain Neville have made 23 appearances between them this term.
"What I've said is that in time we'll look at them," said Moyes on Friday. "They're both at a later stage in their careers but I would certainly be recommending that both of them sign for at least another 12 months if possible.
"You have to make sure that they're both able to contribute. No matter who they are, I'm not here to be the guy who just says we should keep them here because I like them - I would never do that. But as long as the two of them can continue to contribute, then I think they're worthy.
"They will both have six months to go on their contracts come January, so I would think that, because of the contribution they're both making, it would be worth keeping them for another year.
"But that's a [conversation] for the board and myself to have.
"I think it's also something we need to make sure that Phil and Sylvain [are happy with], that they feel they are good enough and able enough to continue playing at this level for another 18 months.
"Both of them are really good professionals and I would expect them to answer me straight if they think they're capable of doing that."