Having ended Barcelona's run of three successive Spanish titles with a record-breaking domestic campaign, Los Blancos are now hoping to reclaim the top prize in club football
Los Blancos have now gone a decade without winning the Champions League, and claiming 'La Decima' has become something of an obsession for the club.
And, after breaking Barcelona's stranglehold on La Liga, Alonso admitted that he is desperate for European success.
"We had a brilliant championship campaign," he told reporters at a promotional event in Indonesia. "We won the title with 100 points. And we also beat Barca.
"But next year I hope to win the Champions League. But we will work very hard to win the three major competitions: La Liga, the Champions League and the Copa [del Rey]."
Alonso is currently in Jakarta with his wife and he admitted that he has been overwhelmed by the reception that he has received from local supporters.
"I am very happy to be in Indonesia," he enthused. "I have been so very warmly received. It was memorable because it is the first time I've been here."
Alonso, who played his part in Spain's Euro 2012 triumph in Poland and Ukraine, arrived at the Santiago Bernabeu from Liverpool in 2009.