The Brazilian midfielder signed for Los Blancos from AC Milan in 2009 and has made 105 appearances, scoring 26 goals.
Mourinho told Rai: "At Real Madrid we never saw the real Kaka.
“He must be happy and Milan could be a good solution, but he is a Real Madrid player."
Ahead of his 50th birthday, the former Chelsea and Porto coach also talked about his future in coaching and a possible return to an old club.
"Now I am 50, I could still coach for at least more 20 years and many things can happen. Maybe [I could] come back to Inter, why not?"
Mourinho also spoke about the Champions League campaign and focused on Juventus as a particular threat, although his team are set to face Premier League leaders Manchester United in the last 16.
"Juventus are a top team," he said.
"It's easy for them to say that they are not the team to beat in the Champions League, [and although] a lot of people say that the favorite teams are Real Madrid, Man United and Barcelona, I say that Borussia Dortmund, Bayern and Juventus can win the Champions League."