Wilshere made his Premier League debut for Arsenal in 2008 as a 16-year-old, and was widely tipped to become a driving force in the club's midfield.
A series of injuries has subsequently stunted his progress, and Wilshere has come in for criticism recently over a perceived lack of development.
Both Paul Scholes and Jamie Carragher - now working as TV pundits - have questioned whether the 22-year-old has lived up to his real potential, leading boss Wenger to come out in support of his player.
"I believe at the moment he should not respond to the criticism, just focus on his game," said the Frenchman.
"If Wilshere can maintain his fitness, 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. I told him the target is for him to have the whole season being available to play.
"Before he [Wilshere] was in Calum Chambers' position [as a promising youngster], then suddenly when you get to 22, the expectation level comes on you. [Wayne] Rooney has gone through that, now it goes through Wilshere.
"He is not [progressing] as far as everyone expected him to be from when he was at 18, but that is because he was injured, not because he doesn't train seriously.
"He is a guy who when he goes out there, he wants to play, he works hard but he was out for one and a half years."
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