The former Chelsea boss helped Real break Barcelona's dominance at the top of Spanish football by winning the Primera Division title for the first time in four years this season, but they fell at the semi-finals of the Champions League for the second consecutive season since Mourinho took charge.
And he is now looking to make history by recreating his success with Porto and Inter Milan and claiming Real's 10th European crown.
Speaking on a promotional visit to Indonesia, he told AS: "I want to win the Champions League with three distinct teams. Now Real Madrid has won the league, the objective for next season is to win the Champions League."
However, Mourinho denied that should he succeed in achieving that goal he could take charge of the Portuguese national team in the near future.
"I don't believe I could manage a national team that only plays a game every two months and an official tournament every two years. I need the pressure of facing two or three games every week."