The 26-year-old is under contract at Chelsea until 2020 and has been rumoured to be in negotiations to extend the deal he signed in February 2015.
Hazard, who joined Chelsea from Lille in June 2012, has been continually linked with Real in recent seasons, mainly due to his long-term respect for Zidane, the head coach of the Madrid side.
"Zinedine Zidane would be a dream to have as a coach," Hazard told RTL in his native Belgium.
"He was my idol when I was little, I have a lot of respect for him.
"Of course I don't know what will happen in my career in the future, but to play under him would be a dream.
"At this time, though, I'm happy at Chelsea. I still have a lot of things to do at Chelsea, and I'm focused on Chelsea."
Hazard recovered from an indifferent 2015-16 season to have a major say in Chelsea's title win of last term, in Antonio Conte's first season as head coach.
The playmaker has made a slow start to the campaign due to sustaining a fractured ankle on Belgium duty in June.
Hazard also insisted he would be prepared to play for Jose Mourinho again.
Hazard and Mourinho did not shake hands before last Monday's (AEDT) Premier League contest between Chelsea and Manchester United, which the Blues won 1-0.
Many pointed to the strained relations when Hazard played with a niggling hip/groin injury in the final months of Mourinho's second spell as Blues boss, which ended in December 2015.
But Hazard added: "Playing again under Jose Mourinho would not bother me."