Distin still have a year left on his current contract with Everton, but Moyes is keen for the 33-year-old Frenchman to sign a new deal.
“It is something we will look at in the summer,” Moyes said in The Sun.
“Sylvain has been great for us and the change after Joleon Lescott left has been relatively seamless.
“He’s played all the games, trains all the time and that is a big thing.
“He takes a lot of pride in that and rightly so.”