The Dutchman has been out since suffering what turned out to be a serious ankle injury while on international duty with Holland during November.
Van Persie, who had scored eight goals in 15 appearances before his injury setback, has made a good recovery.
Stricken: Robin van Persie has been sidelined since November
Wenger remains cautiously optimistic the Holland forward could yet play some part in the Gunners' final couple of matches of the season, when they hope to still be chasing domestic and European honours.
'There is still a little chance for Robin van Persie this season,' Wenger revealed in his programme notes for this afternoon's Barclays Premier League clash with West Ham.
'We are following his progress and physically he is quite sharp, but once he is ready to kick the ball again and returns from his rehabilitation, it will still take him another three weeks.
'This means that, even if he came back next week, adding another three weeks on would still take him nearly into May.'
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