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.
Arsenal travel to West Bromwich Albion on April 6 and then host Norwich City a week later.
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.
Wenger, however, refused to point the finger of blame at England manager Roy Hodgson.
"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."
Arsenal have no realistic hope of silverware this season having exited the FA Cup and Champions League in recent weeks, but a good run of form in the Premier League has given Wenger cause for optimism.
The North London club have won four of their last five Premier League games and are fifth in the table, four points behind Tottenham in fourth but with a game in hand. Chelsea are a further point clear in third.
"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."
Reading are second from bottom in the Premier League and seven points from safety but are likely to be buoyed by the appointment of new manager Nigel Adkins, who joined the club on Tuesday.
