Arsenal are sixth in the Premier League after a run of poor form which has seen them win just five times in 2017 in the league.
And Wenger's proud record of qualifying for the Champions League in 19 consecutive seasons is under major threat.
Arsenal fans' Wenger Out campaign hits New York Fri, April 14, 2017
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But Wilshere, who is on loan at Bournemouth, remains appreciative of Wenger's impact on his career.
He told Sky Sports: "He [Wenger] has always been great for me. He put me in at a young age which you don't see a lot at top clubs with all the pressure for trophies.
"He stuck with me and showed faith in me. So for me he's great and I can't imagine Arsenal without him. He has been great for me and that's all I can say.
Jack Wilshere with Arsenal boss Arsene Wenger
"Sometimes a manager can only do so much, as in prepare a team and then the team have to go out there and perform.
"Again all I can say is that he has been great for me. I've been away for a year so I don't know what's happening there, in the dressing room or what training has been like.
"All I can do is help Bournemouth then go back at the end of the season."
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