The England international endured a frustrating first half to the campaign on the whole, being made to settle for appearances in cup competitions.
Wilshere, who spent last season on loan at Bournemouth, has now forced his way into the Gunners' first-team plans in the Premier League and has been one of the Londoners' star men throughout December.
Wenger has yet to formally offer the 25-year-old a new Emirates Stadium contract, but the Frenchman has been left pleased by what he has seen in recent games.
"Give him credit for what he has gone through - it demands some character," he told reporters. "I have a big respect for that because it is all nicey-nicey when you are super talented and everybody says you are the greatest player at 17.
"To come back to that level when you have gone through what he has gone through, shows a special character. What is a very important quality is always to continue to believe in human beings - I believe everybody is alive to fight, so I never gave up on him."
Speaking earlier this week, Wilshere revealed that he is confident of agreeing fresh terms with Arsenal to extend his stay.