Real have been heavily linked with a move for Hazard for some time, while the Belgium international has also hinted he would jump at the chance to join Los Blancos.
The Belgium international is in no rush to move on, but reports in Spain claim that Zidane is in a hurry and wants him on board in time for next season.
It is claimed Zidane has held a meeting with president Florentino Perez when he made it perfectly clear that Hazard would be the number one target of the summer.
Real are willing to let Gareth Bale move on and Zidane sees Hazard as the perfect replacement for the Wales international, who could join Manchester United or Tottenham.
Chelsea will be determined to keep hold but could face a battle as Hazard would no doubt be interested in heading to the Bernabeu if a bid came in.