Madrid won the Primera Division title in 2011-12, picking up a record 100 points from 38 matches, and will kickstart the new campaign with a home game against Valencia on Sunday.
The nine-time European champions will be challenged by Barcelona for the Spanish first division title, and Mourinho is ready for the duel.
"We are not looking to break records, we want to be the champions," said the Portuguese on Saturday. "That is the objective. Each season is different and the most important thing is to always have ambitions.
"If the previous season was victorious, you want to repeat that and if you didn't have great moments, you want to go for them.The feelings are always the same before starting and I want to get started right away – that´s why we have been working all these weeks.
"Being the champion is being the champion and we are aiming at that regardless of whether more or less points are required."
Mourinho added that Madrid are keen on winning the Champions League this term after falling at the semi-final hurdle for the past two seasons in a row.
"The team has reached an important level," he explained. "It won the most difficult league with unequalled stats and an unsurpassed game quality.
"In Europe we reached semi-finals and that meant fighting to the end for the title. We are the same people, we know each other well and we are going to try to maintain the quality of the game, the team spirit and the level of ambition.
"Given all of that we will be candidates to win all the competitions we play in and play to win every time."
Barcelona will also begin their La Liga campaign on Sunday with a home game against Real Sociedad.