The Brazilian international has struggled to settle in the Spanish capital since joining the club in 2009 from AC Milan.
Leonardo, who played alongside Kaka during their spell together in Milan, has dismissed speculation that he is about to be reunited with the 29-year-old.
"There is nothing," Leonardo told L'Equipe. "I have known Kaka for 11 years, and when he joined Milan he could have been loaned to PSG.
"We have a very good relationship but we have never asked Kaka to come here."
Madrid paid Milan a reported £58m for Kaka's signature.