Kaka has recently been linked with a move to the likes of Tottenham and Arsenal.
Kaka scored and created an assist in the 6-0 win over Real Zaragoza on Sunday.
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 (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.”