The England international has shown his best form in glimpses this season, but he concedes that he must make more of an impact in the final third of the pitch as he looks to take advantage of being fully fit for an extended period.
"I've said before that my goalscoring record has never been good enough and that I always want to add more goals," Wilshere told the club's official website.
"You look at the top midfielders in the world like [Frank] Lampard and [Steven] Gerrard who were getting 15 or 20 goals a season back in their day.
"I'm not saying I can get that many because they were specialists at that, but I could definitely get into double figures."
Wilshere has scored just 12 goals in over 150 senior appearances at club level.