The Brazilian playmaker has been linked with a move away from the Santiago Bernabeu due to a limited number of appearances since his move from AC Milan in 2009.
However, a recent run in the side has given the 30-year-old the desire to make his mark on the club.
"Even when there was lots of talk in the summer I did not think about leaving because I was sure I could bring a lot to Real Madrid," he told Estadao.
"I still have three years left on this contract and I think I can contribute. I want to continue at Real Madrid, earn a place in the team and win titles."
Kaka featured for Los Blancos in Wednesday's 4-1 victory over Alcoyano in the Copa del Rey.