The England international has been out with an ankle problem since the beginning of March but has started training ahead of their weekend game at home to Norwich City.
Having been largely written off earlier in the season, Arsenal have the chance to go third in the table with their top-four rivals Chelsea playing their FA Cup semi-final on Sunday while Tottenham Hotspur have no game.
"Jack has joined normal training since Wednesday... [he is] 90 percent available for Saturday," Wenger said on the club website.
After Thursday's Premier League decision to adopt goalline technology for next season, Wenger, a long-time supporter of its introduction, said fears it could slow the game down were unfounded.
"When a referee speaks to a player for two minutes and says, 'be careful because if you come back and make a bad tackle I'll be in a position to give you a yellow card' and doesn't do anything else, you can argue it slows the game down," Wenger told reporters. .
"When a goalkeeper takes a minute over a goal kick, you could argue it slows the game down. I don't believe [technology] would slow the game down at all if it is done in the right way.
"There are a lot of things to work out because if you look at goalline technology, it took them two years to get it right. I'm amazed we are resistant on the principle of moving forward for more justice in our sport.
"If it was to sell more publicity [or] if it was for financial reasons then I don't agree with it. But if it is to get more decisions right then we all have to fight for it."
