Wilshere also believes that he and the 19-year-old winger can form an important combination for the England national team.
"If we can get playing together for Arsenal, then hopefully we can take it onto the international stage and it'll be great for both club and country," he is quoted as saying by the Daily Mail.
"I think that Alex is already mature enough to step in at any level. You could see that at the Euros - he was just 18 but it was like he was meant to be there.
"That confidence is one of his main attributes, and I think that the boss at Arsenal has been really good for him."
Wilshere made his first competitive appearance for Arsenal in over a year in their 1-0 victory over Queens Park Rangers at the Emirates on Saturday.