The Belgium international has been heavily linked with a move to Real Madrid since the start of the current Premier League season.
Hazard has scored 12 times and has made 10 assists in 25 games in the Premier League this season.
The Chelsea FC number 10 is on course to finish with his best goal haul for an individual top-flight campaign despite a difficult season under Maurizio Sarri.
The 28-year-old has been touted as a long-term target for Real Madrid since Mourinho was in charge of the Blues for the second time between 2013 and 2016.
Real Madrid haven’t made a marquee signing to replace Cristiano Ronaldo after the Portugal international moved to Juventus from Real Madrid last summer.
Asked about Hazard’s potential move to Real Madrid in the summer, Mourinho told DAZN as quoted by the London Evening Standard:
“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.
“[But] talking of talent… Does he have the talent to play for Real Madrid? He does.
“Does he have the personality to wear a shirt that weighs so heavy and to play in front of a crowd like the Bernabeu? Yes, he does.”
Hazard scored a stunning panenka penalty in Chelsea FC’s shootout defeat by Manchester City in the Carabao Cup final at Wembley on Sunday evening.
The Blues are in sixth place in the Premier League table and three points adrift of Arsenal in fourth spot.
Chelsea FC will take on Tottenham at Stamford Bridge in the Premier League on Wednesday night.