The French legend made the shock decision to step down as manager on Thursday.
Having won the Champions League for a third successive season, Zidane opted to call time on his spell in charge at the Bernabeu.
Real now face the prospect of searching for a new boss with the transfer window already underway.
Hazard is a long-term target of Real, and the Belgium international was attracted by the possibility of working under his hero.
Chelsea fans may have been relieved to see Zidane leave as they hope to keep Hazard at Stamford Bridge.
Chelsea do not have Champions League football to offer this season and are edging towards crisis.
Owner Roman Abramovich could step away from the club over his visa dispute, while Antonio Conte’s position remains unclear.
It is unclear who will be at the helm for the Blues come the start of the season, similarly with Real.
However, they have a key target in mind with Tottenham boss Mauricio Pochettino the No.1 choice.
Despite having just signed a new long-term contract with Spurs, president Florentino Perez regards the Argentinian as his favourite to replace Zidane.
Pochettino would potentially sacrifice taking Hazard to the Bernabeu in favour of Harry Kane, Don Balon add.
Hazard’s contract at Chelsea expires in 2020, and he has been looking to see what players come in before sorting his future.
But the Blues may well cash in with Real having long wanted the 27-year-old forward.