The Brazil international was at the weekend linked with a loan move to either White Hart Lane or Emirates Stadium after an injury-hit two years at the Bernabeu.
But Kaka, who scored and created an assist after coming off the bench in Real's 6-0 thrashing of Real Zaragoza on Sunday, has reiterated he is going nowhere.
He told AS: "I am very happy with the game. To start the league by winning six goals to zero, and with a goal and assist, is magnificent.
"As I've always said, I want to stay in Madrid. All that I can say is that reports of my father talking to other clubs are a lie.
"The coach (Jose Mourinho) said in yesterday's news conference of how he is counting on me this season, and that gives me peace of mind.
"The team shows it is strong. The performance was good in every way. We played well in the Super Cup and have started the league in the best way possible.
"However, we will still go slowly and focus on doing things the same way every week."