Chelsea boss Maurizio Sarri said last month that Hazard was free to leave the Premier League club if the 28-year-old had his heart set on a move.
"Does he have the talent to play for Real Madrid? He does," former Real boss Mourinho, who managed Hazard at Chelsea from 2013 to 2015, told sports streaming service DAZN Espana.
"Does he have the personality to put on a 'super-heavy' shirt and play in front of the fans at the Bernabeu? Yes, he has the personality.
"Regarding Eden's ambitions... be it playing for Chelsea his whole life or playing for a giant like Real Madrid, I can't say, because I haven't spoken to him for a long time."
Mourinho, who has been working as a television pundit and soccer show host since being sacked as Manchester United manager in December, also said he wanted to return to football management before the start of next season.
"In this short phase of my life, which I hope is only until June, I'm more concerned about what others would do than what I would do," he added.
(Reporting by Hardik Vyas in Bengaluru; Editing by Simon Jennings)
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