Van Persie has made just two appearances for United since he scored the only goal against former club Arsenal at Old Trafford in early November.
He has not featured since a substitute's outing against Shakhtar Donetsk in the UEFA Champions League last month and has sat out the Premier League champions' last nine games.
Reports had claimed the 30-year-old would be out for another six weeks, but Moyes dismissed those reports about the Netherlands international's fitness.
"I don't know where that has come from," said Moyes after United's 2-0 home win over Swansea on Saturday. "That would be wrong information as far as I am concerned."
Speaking before the game, Moyes confirmed that Van Persie has recently been back in his native Holland to undergo treatment on the injury.
The United boss added: "We're trying to get Robin back. He's got a thigh strain similar to the one he had at Arsenal [in the second half of the 2007/2008 season].
"He never had an injury all last season. He took a corner against Shakhtar and felt his thigh so it was a freak thing really and not [aggravating] an injury he'd had before.
"It's a different injury. We have to manage it correctly and he's been to Holland to see a guy he works with there. So we're doing everything we can to give him the right treatment and get him back as soon as we possibly can. But I don't want to put a date on his return."