Bayern last held the final in 2012 and featured in it only to be beaten by Premier League side Chelsea, who won following a penalty shoot-out.
"I can confirm that Bayern, together with the city of Munich, will officially apply to host the 2021 Champions League final at the Allianz Arena," said Bayern chief executive Karl-Heinz Rummenigge.
"Despite the disappointment of the defeat to Chelsea in 2012, we still look back fondly on the 'Finale dahoam' [final at home]. We would be very grateful if UEFA gave us the opportunity to again welcome the football world to Munich."
associations have expressed interest in hosting a UEFA club final in 2021— UEFA (@UEFA) November 1, 2018
N. Ireland - Belfast
Krestovsky Stadium, the home of Russian club Zenit, is the only other contender to host the 2021 Champions League final, UEFA confirmed.
Seville, Vienna and Tbilisi are the three cities bidding to be hosts for the Europa League final in 2021, while Belfast, Kharkiv, Minsk and Helsinki are in the running for the UEFA Super Cup.
Gothenburg and Prague are hoping to be selected for the Women's Champions League final.