A number of prominent figures in the game, including former England midfielder Paul Scholes, have questioned the pace of Wilshere's development since breaking into the first-team squad as a youngster, but Wenger is confident that he will realise his potential.
"Before he was in [Calum] Chambers's position, then suddenly when you get to 22, the expectation level comes on you," the Gunners boss told reporters. "[Wayne] Rooney has gone through that, now it goes through Wilshere.
"I believe at the moment he should not respond to it, just focus on his game. If Wilshere can maintain to be fit physically, then he will make a huge career.
"At the moment, I believe he should just focus on that - being fit, present and to improve physically. The rest will come along."
Wilshere is expected to keep his place in the Arsenal side for Saturday's trip to Goodison Park to face Everton.