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Wenger has been heavily criticised by Gunners fans after failing to make any significant signings since the end of last season.
Offers for Gonzalo Higuain, Wayne Rooney, Luis Suarez and Luiz Gustavo were all snubbed and that created a poisonous atmosphere as fans vented their frustrations during Saturday's 3-1 home defeat against Aston Villa.
Some pundits feel Wenger is likely to walk away from the Emirates Stadium if the criticism continues, but Wilshere responded by revealing he might be forced to go as well if that were the case.
"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 told 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."
Wenger earned some breathing space with Wednesday's 3-0 victory at Fenerbahce, a result that has put Arsenal on the brink of qualification for the group stages of the Champions League.
Eight years have passed since the Gunners last won any silverware, but Wilshere is adamant the north London club will win a major trophy as long as Wenger is given some breathing space.
"We have lost a few strong, big-name players in recent years and that's hard for any club," Wilshere added.
"First we lost Thierry Henry and then Cesc Fabregas, Samir Nasri and Robin Van Persie.
"That's hard, especially when Robin went to another team in England, it makes it harder for us to compete.
"But now we've got a good crop of young English players coming through and if we stay together and build something then we can win a trophy in the next few years."
