The former Santiago Bernabeu player and coach says he recommended the World Cup winner taking over to president Florentino Perez
Former Real Madrid player and coach Bernd Schuster has tipped Germany coach Joachim Low to take over in the summer.
Although the Champions League holders only recently hired current boss Santiago Solari on a contract that runs until 2021, there have been reports they are looking for a bigger name to replace him in the summer.
Jose Mourinho, recently sacked by Manchester United in December, has also been linked with a return to the Santiago Bernabeu, while they are also interested in luring Tottenham's Mauricio Pochettino to the Spanish capital.