Rooney, who has not played since the New Year's Day defeat by Tottenham Hotspur, has returned to the club from warm weather training but will not be available to face Jose Mourinho's team.
"He's training, doing some running and looking quite good. I don't want to put a date on his return just now as I don't want to say he'll be fit for whatever game and then find he's not. We've just got to take it bit by bit," Moyes told a news conference.
Moyes sounded more confident about Van Persie's fitness.
"I'm hoping Robin has a good chance of training at the start of next week. It would be a great boost. Most of the players are getting close to full fitness," Moyes said.