The Toffees are on the hunt for a new manager, following the departure of Roberto Martinez.
Everton are reportedly set to interview Moyes, with rumours that he could return to Goodison Park picking up legitimacy.
And Distin, who teamed up with Martinez at Everton, feels that the Scottish boss would be a good addition for his former side.
“I think it would be a good thing for the club for him to go back,” Distin said, when asked whether Moyes could return to Everton. “It would bring back some stability again.”
Moyes spent 10 years at Everton earlier in his career, before he agreed to take over at Manchester United.
His time at Old Trafford was not a success, and he also struggled to make an impact at Real Sociedad.
Moyes has been out of work since leaving the La Liga side, and Everton are said to be considering putting him back in charge.
Frank De Boer, Manuel Pellegrini and Ronald Koeman have also been linked with the job at Goodison Park.