The Netherlands international has been struggling with toe and groin injuries in recent weeks and missed United's Champions League clash with Bayer Leverkusen and the 2-2 draw with Tottenham at White Hart Lane on Sunday.
The champions face Roberto Martinez's high-flying Toffees on Wednesday and, when asked if Van Persie could return, Moyes told a pre-match press conference: "Robin's okay. He's got a chance."
United go into the game two points behind Everton, having drawn their last two Premier League games, and the Scot hopes to see his side return to winning ways.
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"But we still drew two games and won one last week. We'd like that to be a better ratio but nevertheless it's not a bad one either."
The match sees Moyes face his former side and he took time to praise Martinez's impact at Goodison Park.
"They have a new manager there and he's brought in his own players as well. Roberto Martinez has done a really good job," he observed.
"I had a great time at Everton - they were fabulous to me - but I'm manager of Manchester United now."