Assistant coach Aitor Karanka has given the clearest indication yet that Real Madrid want to replace Kaka with Tottenham's Luka Modric this summer.
Modric has returned to training with Spurs this week, having been fined by the club for skipping sessions as he sets his sights on a move away from White Hart Lane this summer.
Manchester United and Paris St Germain have both been linked with the Croatia playmaker, with Tottenham believed to be holding out for a £40million fee.
But Real appear his likeliest destination, a move which would allow Brazil international Kaka to end a largely ineffective spell at the Bernabeu.
Big-spending PSG have also been mooted as the 30-year-old's next stop and he did not travel with Real for tonight's friendly away to Real Oviedo, which they won 5-1.
Karanka told AS: "We decided he would stay in Madrid. Kaka and the club are working to find a good solution for all parties."
Asked about Modric, he added: "Which club would not want a player like him?
"He is an outstanding footballer and had a great tournament (Euro 2012). It is clear that he would fit in Madrid."