Wenger has come under fire for the Gunners' failure so far this summer to make any significant signings after failing with approaches for Gonzalo Higuain, Wayne Rooney, Luis Suarez and Luiz Gustavo.
The fallout from the 3-1 defeat by Aston Villa last Saturday saw the Arsenal Supporters' Trust declare it would be "inappropriate" for the board to offer him a new contract until the transfer window closes.
In comments published online, Wilshere insists should Wenger depart the club it might affect his own future.
"I want to win things with Arsenal and I want to be there in the future, but if the boss leaves then things could change," Wilshere is quoted as saying to Zapsportz.com.
"Arsenal are always in my heart and by signing a deal for the next five years shows my commitment to them and their commitment to me so at the moment everything is good.
"Arsene Wenger has been there for so many years and he's always delivered trophies.
"OK we've had a little dip in the last five or six years, but he's a great manager and people who question his ability are ridiculous.
"He's qualified for the Champions League for 16 years so I think he's the right man for the job."