The Holland striker has been on the sidelines since suffering a serious ankle injury while away on international duty in November.
Van Persie, who had scored eight goals in 15 appearances before his setback, has made a good recovery, and has now returned to the Gunners' London Colney training complex to complete his rehabilitation.
Mixed fortunes: Robin Van Persie (right) enjoyed a flying start to the season.
Wenger remains cautiously optimistic the 26-year-old could yet play some part in the final few matches of the season, when Arsenal hope to still be chasing domestic and European honours.
However, the Gunners boss declared: 'Do not expect miracles when a guy has been out for such a long time.
'We are, though, happy to have him back and he is physically, fitness-wise, in good shape. We have just to get him back to full team fitness - that will take two to three weeks maximum.
'After that you have to get a few games to get back to your best. It is very difficult to predict. Physically it looks all good, but after that when he plays in games you have to see how his ankle responds.'
Van Persie even went to Serbia for radical treatment using massage with a horse placenta to try to help the healing process when he discovered the true extent of his injury.
.but has been missing since November after being injured playing for Holland
Wenger reflected: 'When you are hit by injury, the first three weeks are very difficult. I believe that is behind him now, once you start to practice again. The most important thing at that age is to be tired at night - when you can train, you can deal better with the frustration.
'When you lie at home at the start of your injury and cannot even do anything, it is very frustrating. I believe the hardest time is behind him.'
Defender William Gallas, meanwhile, is another player who is on the recovery trail having missed the past seven matches because of a niggling calf problem.
'He is back today from his rehabilitation and will be back in full training over the next couple of days,' said Wenger. 'But he is too short to be available for the weekend of course and certainly as well for Barcelona game on Wednesday.
'We have to assess him, it is too early to say [whether he is available for Wolves].'
Title chasers: Van Persie could return to aid Arsenal's hunt for the league crown
Gallas, 32, has yet to agree a new deal with Arsenal, and can talk to other clubs as he is out of contract in the summer.
Wenger said: 'In the next two or three weeks we will not deal with any contract because we have games every three days and we will focus on our targets.
'I feel we are winning the battle to keep him, but in this domain you have to be open and be ready for anything.
'He is in a position where he is free to sign for anybody he wants. Tomorrow somebody could come up and offer him a massive amount of money and I don't know if he will sign or not.
'William knows we want to keep him and that we make an effort - but it has to be, as it always has been historically, within our set budget.'
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