The Dutchman has been on the sidelines after he picked up a serious ankle injury while playing for his country against Italy last November but is now closing in on a return.
Van Persie had confirmed on Monday that he hopes to be back training with the Gunners this week and while Wenger has confirmed that could be the case, the Frenchman has also said they will not rush him back into the first team.
"I think he will be back (with the club) this week," Wenger revealed. "We sent our fitness coach out to Holland where Robin has been having his rehabilitation.
"Physically he looks very sharp, but we aim at least to wait a month."