But van Persie revealed earlier on Monday that he was back in light training and was confident he would be fully fit before the end of the season.
Wenger is also pleased with the 26-year-old's recovery and will be keen to welcome the forward back as Arsenal chase Premier League and Champions League glory.
The Gunners boss, however, will not rush Van Persie, telling their club's official website: "I think he will be back (with the club) this week.
"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."
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