The 24-year-old has returned to training with the rest of the Arsenal squad following a spell of rehabilitation in his native Holland, as he recovers from a thigh problem - the latest fitness setback of an injury-plagued season.
After recovering from a bout of flu, medical tests revealed the thigh problem had flared up again and Wenger decided to give the disappointed Dutchman a complete break with a spell away to help his recuperation.
Van Persie will not feature in this weekend's clash with Manchester City, but could be eased back in time for the UEFA Champions League clash with Milan on 20th February.
The Arsenal chief, however, will not be taking any sort of gamble on a player who has been limited to just 13 starts this season.
"After last time we have decided not to push him and give him the needed time. It has all gone well," Wenger said.
"I don't want to set any timescale because that means, if he is not ready by that date, I might feel I have to push him."