David Moyes is hoping to have the Dutch striker back in action in the New Year, while Wayne Rooney is expected to face Tottenham despite carrying a groin injury
Van Persie has struggled with thigh, toe and groin injuries this season and suffered his latest problem while taking a corner in the Champions league against Shakhtar Donetsk.
But Moyes, who has overseen six consecutive victories for his side in all competitions, has indicated the striker is "not too far away" from a recovery.
"Robin’s started some light training and he might not be too far away," Moyes told reporters.
"We’ve not had Van Prsie and Rooney as a partnership very often and we are looking forward to getting them back together."
Rooney, meanwhile, is likely to be fit to face Tottenham on New Year's Day, after the England international has been carrying a groin injury.
Moyes added: "I would expect Rooney to be back for Wednesday, hopefully. But he’s got an adductor injury in his groin, which kept him out of the Stoke game in the League Cup.
"Ideally we would like to give it a bit longer than three or four days between each game, but we are not getting much time at this point of the season."