The Gunners have not won a trophy for eight years and Wilshere knows that the fans are unhappy.
"It's a big season ahead for us," Wilshere told Sports Illustrated. "A few of the other big teams have changed managers this season and we've got a manager who has been there a long time.
"We haven't won a trophy in seven or eight years. The fans are starting to realise that and we're feeling the pressure, and we have to step up.
"I think we [are ready to challenge for the title]. We could maybe add a few more players that when we're getting tired we can change things up. That's a big thing in England, you have to have a big squad."
Arsenal are currently on their pre-season tour of the Far East.