The duo have not yet played together for the Gunners, with Wilshere missing the whole of last season through injury after Oxlade-Chamberlain joined the club in August 2011.
Wilshere, 20, made his first appearance for Arsenal in 14 months during the 1-0 win over Queens Park Rangers on Saturday.
And the England midfielder is looking forward to developing a partnership with the 19-year-old winger, who is currently sidelined with a hip problem.
“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,” Wilshere told 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.”
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