The London club's defeat by second-tier Blackburn Rovers in the FA Cup on Saturday ended hopes of domestic silverware and a poor result at home to the Bavarian giants on Tuesday would all but guarantee an eighth successive trophy-less season.
Wilshere, who played the final 20 minutes against Blackburn after being rested for Tuesday, says Arsenal need only look at Chelsea's feat last season for inspiration.
Chelsea were also struggling in the Premier League but some impressive backs-to-the-wall displays in Europe saw them past Barcelona en route to beating Bayern in the Champions League final in the German club's back yard.
"Chelsea are an inspiration for everyone," Wilshere was quoted as saying in British media on Monday. "They weren't having a good season and OK, they got a bit lucky in some games, but they showed great character and we need to do that.
"We need to come together as a team."
Arsenal were booed off the pitch against Blackburn after a late goal from Colin Kazim-Richards inflicted a second loss this season to lower-division opposition on Arsene Wenger's side.
They also face a battle to finish in the top four of the Premier League and there is growing discontent among the club's fans who pay the highest ticket prices in England.
Wilshere, who has recently returned from a year-long absence with an ankle injury, said Bayern's visit offered the ideal chance to show some fighting qualities.
"We have to regroup now," he said. "We need everyone behind us. We know what Bayern are capable of; they have a great team.
"We've beaten big European teams here before so we need to do it again. Just now it would be a bit pretentious to say that [we can win the Champions League] but you never know.
"We have to give it a good shot on Tuesday night and see where we stand afterwards."
