Wilshere, who has 28 England caps but has endured a stop-start career punctuated by a number of injury problems, has been out since suffering a leg fracture in the close season.
He has returned to Arsenal training but with only eight games of their season remaining, faces a race against time to prove his fitness.
Wenger, however, said it would not be a gamble for England manager Roy Hodgson to include him in his squad for the European championships in June and July.
"It's very important for his confidence that he can go to the Euros and he can play. It's also important to have a player of his quality available," Wenger told reporters.
"If he's completely fit, no (it's not a gamble). When you're a national team coach, you can take a gamble on one player but certainly not on five. Roy Hodgson has to consider the whole situation. You can certainly take a chance on just one player.
"I'm cautious with Jack now but to be back fully competitive, it will take a few weeks," added Wenger. "Once he is completely fit and competitive he will be available for Arsenal and for the national team. Why not?"
A run of two wins in nine games in all competitions has left Arsenal with only an outside chance of claiming silverware from a season that promised so much but has imploded at a crucial time.
Since they beat league leaders Leicester City 2-1 on Feb. 14, Arsenal have exited the Champions League to Barcelona, dropped 11 points off the pace in the Premier League and were knocked out of the FA Cup by Watford.
Arsenal face Watford again in the league on Saturday and anything other than victory would hammer another nail in their prospects of a clinching a first Premier League title since 2004.
Wenger has not ruled out a late push, however, and their performances in their last two games, a 3-1 Champions League defeat to Barcelona, and a 2-0 league win at Everton, have given him hope.
"It has been very difficult but I believe you focus on giving your best and performing. Our last two games were very positive and it shows the team responds well.
"Some teams sink and some respond. We have responded in a very efficient way."
(Reporting by Toby Davis; Editing by John O'Brien)
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