The German giants are next up for the Gunners at the Emirates Stadium on Tuesday - and the soon-to-be charges of Pep Guardiola are firm favourites to progress.
But Wilshere believes Arsenal are capable of emulating Chelsea's unlikely success when the Blues beat Bayern on penalties in the final.
"Chelsea are an inspiration for everyone. They weren't having a good season and, okay, they got a bit lucky in some games," said Wilshere.
"But they showed great character and we need to do that. We need to come together as a team.
"We have good leaders here, a good team atmosphere. That will help us.
"We have a good bunch of lads in the dressing room. They're winners as well, the likes of Lukas Podolski and Mikel Arteta. They want to win.
"We know what Bayern are capable of. They have a great team. We need everyone behind us and we go again.
"We have beaten big European teams here before so now we need to do it again."
Thomas Vermaelen is also confident ahead of the Bayern clash, despite Arsenal's shock FA Cup defeat to Blackburn at the weekend.
"The result against Blackburn was terrible," he said.
"It's normal the fans are disappointed but we need them to believe as well. We need their support 100 per cent on Tuesday.
"Anything can happen in the Champions League.
"Is it realistic to win the Champions League? Why not? It's a tournament, I believe in our chances."