The Londoners have not won a major trophy since 2005 but are two points clear at the top of the Premier League, as well as still being in the hunt to win the Champions League and the FA Cup.
Their only addition in the January transfer window was Kim Kallstrom, who is already unavailable due to injury, but the England international is unworried.
Wilshere told The Sun: "People keep saying we need a new striker, but Olivier Giroud has been great and Lukas Podolski can play there. Aaron Ramsey and Santi Cazorla have scored a few. Even I've got a couple! We know we can create chances and score goals.
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"It would mean a lot to win something. Everything, to be honest. To win something for the first team would be amazing, not just for us but the fans. I grew up watching Thierry Henry winning everything, the 'Invincibles' and all that.
"This year, I feel we are right in there. We beat Spurs in the third round of the FA Cup and showed everyone we are focused in that competition. The Premier League and the Champions League - anything can happen. You saw that when Chelsea won it [in 2011-12].
"This season we have a bigger squad. When one goes out, another comes in. It has happened many times. [Alex Oxlade-Chamberlain] has come back and is looking good. He is like a new signing, going into the last few months of the season. Podolski is getting fitter.
"A few players are out but we still have a good squad."