The newspaper says that the Spanish side have rejected the deal and demanded a further €10 million (£9 million) for the midfielder. Madrid signed the player for €68.5 million (£60 million) from AC Milan just two years ago.
Kaka, who spent a large part of last season out on injury, recently said he wanted to stay with the club to repay Jose Mourinho for his support.
“My desire is to remain at Real Madrid,” he said. “I knew there would be speculation because since arriving in Madrid I have been linked with ten teams. But Mourinho wants me to continue and I will follow.”