The Spain international has set his sights on the Champions League trophy, but guaranteed he is not expecting an easy match on Wednesday.
The Spanish side's last success in the UEFA competition came 10 years ago, when it defeated Bayer Leverkusen. Since then, the club has gone to the quarterfinals twice and lost to rival Barcelona in the semis last season.
And though La Liga is one of the few prestigious competitions Alonso has not yet won in his career, he conceded that winning the Champions League is his biggest wish.
"La Liga and the Champions League are the most important competitions. I am still missing La Liga and we want to win it, but everyone is eager for the Champions League," he said.
Real Madrid has been drawn with Lyon, Ajax and Dinamo Zagreb, with the club's first game at the Croatian club's arena on Wednesday. Alonso stressed his side is not hoping to find the three points gift-wrapped in Zagreb.
"We have been analyzing Dinamo, I believe they got off to a good start in the league," he said. "They have not been in the Champions League for many years and to meet Madrid is an extra motivation for them. We expect a difficult match."
