The former Spain international signed a two-year deal with Bayern last week, joining from Real Madrid, and made his debut for the club in Saturday's 1-1 draw with Schalke.
The 32-year-old says he is desperate to go all the way in European club football's elite competition again before he hangs up his boots.
"It would be a dream come true to win the Champions League with a third team," the experienced midfielder said at a press conference.
Alonso added he is happy to join the Bavarian giants this summer and was delighted to make his debut against Schalke.
"I was very excited to make my Bayern debut and really enjoyed it. I was quite surprised that I started right away, but it was a decent debut.
"It is an honour and a privilege to be here in Munich. I immediately got on a plane when the clubs reached an agreement.
"Over in Spain, football fans are getting interested in the Bundesliga more and more. The league is getting stronger and its great to play here. I want to prove something to myself here. It will be a great experience."