The London club have not won a major trophy since 2005, but have given themselves an excellent chance of putting that right in the current campaign.
Arsene Wenger's side are two points clear at the top of the Premier League, as well as still being in the hunt to win the UEFA Champions League and the FA Cup.
England midfielder Wilshere is confident they can avoid being left empty-handed again come May.
He 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.
"The next two months are really important and if we come out of those unscathed, we will have a real chance.
"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 the 2011/12 season).
"This season we have a bigger squad. When one goes out another comes in. It has happened many times. Ox (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."
Arsenal's Premier League credentials will be tested when they travel to fourth-placed Liverpool on Saturday.
