Van Persie was ruled out of Sunday's game at Manchester City with a groin strain.
Moyes confirmed the Dutch striker was unavailable due to the injury but played down its significance and is confident of having the player available for midweek action.
"He was nursing a wee bit of a groin strain during the week," Moyes told Sky
Sports 1. "We thought he might be okay, but not quite.
"We gave him every chance, he had a real good opportunity of making it.
"It's nothing serious, it might keep him out for a few days but it's not too
bad. He might be okay for Wednesday or maybe next week."
United face Liverpool in the Capital One Cup on Wednesday and West Brom in the Premier League on Saturday, with both games at Old Trafford.