The Man U boss says the Dutch striker could make his return from injury at Old Trafford. Moyes also praised Toffees successor Roberto Martinez for the job he has done to date.
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 now host Roberto Martinez's high-flying Toffees at Old Trafford and, when asked if Van Persie could return, Moyes told a pre-match news conference: "Robin's okay. He's got a chance."
United go into the game two points behind Everton, having drawn its last two Premier League games, and the Scot hopes to see his side return to winning ways.
"The job is to keep it going, keep winning and keep on a good run of form," he said. "We've done that but, as I've repeated myself many times, we let in a late goal at Cardiff which turned what would have been a really good week into one that wasn't quite as good as we would have liked.
"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 for the first time as United boss, and he took time to praise Martinez's impact since suceeding him 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 said. "I had a great time at Everton - they were fabulous to me - but I'm manager of Manchester United now."