The Gunners have had a torrid start to the season, having failed to impressing the Premier League, and they were knocked out of the Capital One Cup by League Two Bradford last week.
Many believe time has run out for Wenger but Wilshere claims the Frenchman just needs time to turn things around at the Emirates.
"For me, there is no question he is the right man. You cannot start questioning him because we have had a few bad results. The players have to look at themselves," Wilshere said.
"Every year he has been in the Champions League and there is no other manager who has done that. He has built a legacy at this club. He changed everything from when he came in 15-16 years ago. He brought the Total Football, if you like, to Arsenal - the passing game.
"He has also been great for me, has shown great faith in me from when I was young. He stuck with me when I was injured and has still stuck by me."
The Arsenal star added that he is ready to sign a new deal at the club which he joined as a 9-year-old.
"I am talking to the club and I probably will be committing my future to the club in the next couple of weeks," he said.
"I know the team are going through a bad stage at the moment, but that is like any team."
The 20-year-old also sees no reason why Arsenal cannot turn things around in 2013.
"We can still realistically win everything we are in. I know we are a long way behind in the Premier League, but football changes quickly," Wilshere added.
"If we win three games and another team loses a couple and draws one, we are back in it. It is not in our hands so we need a bit of luck.
"We are in the last 16 of the Champions League, that is going to be difficult, but we know in the Champions League anything can happen. It is two games and we can beat anybody. We showed that at home before when we beat Barcelona. There is no reason why we cannot do it again.
"We have got a hard game against Swansea in the FA Cup, but if we win that and a couple of big teams go out, anything can happen in cup football."