The England international has been out with an ankle problem since the start of the month, but it had been rumoured he was in line for a weekend return.
"Regarding Jack? I think two weeks on Sunday. Not the next game, but the game after," Wenger told reporters.
The 21-year-old playmaker's return can not come soon enough for Arsenal who are battling London rivals Tottenham Hotspur and Chelsea for Champions League qualification.
Left-back Kieran Gibbs is a doubt for Saturday's home match with flu while forward Theo Walcott is definitely out, having suffered a muscle tear in training while on international duty with England.
"Walcott is an accident that could have happened here," Wenger said.
"I have no conversation with the England manager. He uses the players how he wants to use them."
"We've got nine games to go, five at home and four away. The form we showed against Bayern [in the Champions League last 16 second leg] was very good. We have a chance to finish in the top four," Wenger said.
"We have the experience of a few years and a special desire to do it together. It's a good opportunity for us. We want to grab this chance. If we are consistent we will do it. We're not focused on Tottenham, but the way we want to play."
