The Belgium captain has recently been dumped out of the World Cup by France after a 1-0 loss in the semi-finals.
Chelsea star Eden Hazard has admitted Real Madrid remain a "dream" club, even without the presence of former manager Zinedine Zidane, amid persistent rumours linking the Belgium global with Los Blancos.
Elsewhere, Neymar and Robert Lewandowski have moved down the list after the World Cup, while Kylian Mbappe is unlikely to leave PSG any time soon.
But despite Zidane having been replaced by Julen Lopetegui, Hazard told beIN SPORTS his thinking had not really changed.
"I know him well, I know that when he makes a decision, he does so knowing all the consequences".
But Hazard believes Madrid are still an attractive destination for any footballer in the world, even without legend Zidane at the helm.
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With six goals so far at the World Cup, Kane looks a dead cert to take home a golden boot, and after over 100 Premier League goals in just five seasons, he is said to be an "excellent replacement".
"Thanks to all and, of course, as I said that first time in our stadium nine years ago: Hala Madrid!"
The former banker has already agreed a contract with Chelsea and has discussed the club's transfer policy at length with the hierarchy, with only a deal between the Blues and Napoli standing between him and becoming the next manager at Stamford Bridge.
Perez is desperate to sign Neymar too but Hazard appears the more likely signature at this stage, with Diario Gol reporting that No. 7 spot has been reserved for the Chelsea man.
And it is that kind of ambition that will keep the Belgian in London, who wants to win the Champions League.