Van Persie sat out Wednesday's Champions League victory over Real Sociedad with a combination of niggling problems.
But it appears the Dutchman's absence will be a brief one.
"Robin has a good chance," said Moyes. "He had a problem with his toes and a little bit with his groin. But he has had a little bit of training as well and he should be okay."
Moyes confirmed experienced defenders Nemanja Vidic and Rio Ferdinand were also progressing well.
However, England duo Danny Welbeck and Tom Cleverley remained on the sidelines.
"Danny has fluid on his knee," the Scot said. "Tom is still recovering from his calf."
Moyes refused to comment on reports United were set to offer striker Wayne Rooney a contract extension.
However, the Scot did admit Rooney was in top form at present.
"It's been great working with Wayne because he's an excellent footballer," he said. "I've said from day one he's been great. He had a very good game in midweek.
"We want that form to continue. We want him to keep scoring goals. He is a big plus for us just now. I don't think it's me or anyone else. It's Wayne Rooney. He had to make sure he was the best he could be and he's done that.
"He's in good nick, his talent is unquestionable. He's physically very good, mentally in a good place and his form has been
After losing three times already this season, and recording only one victory in their four Premier League home games, United have fallen off the pace and head into the weekend eight points adrift of pacesetters Arsenal.
Stoke manager Mark Hughes on Thursday suggested his old club could not afford any further slip-ups and that there was an air of vulnerability about them that did not exist under Sir Alex Ferguson.
Evidently, Moyes does not agree.
"That might be Mark's opinion," said Moyes. "He's entitled to that but we'll wait and see. There's only two months of the season gone and there will be a lot of slip-ups by teams between now and the end of the season. We don't want to lose many more if we can help it."