The Belgium international has been heavily linked with a move to the La Liga giants at the end of this season, and said earlier this month that a decision has already been made on his next move.
Mourinho, who managed the 28-year-old at Chelsea following his spell as Madrid boss, believes they could be a good match.
“Eden's ambitions, playing at Chelsea his whole life or going out to a giant like Real Madrid,” Mourinho said to DAZN.
“I can't tell you, because I haven't talked to him for quite a while.
“Let's talk about talent. Does he have the talent to play for Real Madrid? He does.
“Does he have the personality to wear a super heavy shirt and play in front of a crowd like the Bernabeu? He has personality, yes.”
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