Madrid, who have been drawn against Paris St Germain in the Champions League last-16, are fourth in the league and enduring a disappointing domestic campaign.
RMC fails to reveal the details of the deal between Real Madrid and Hazard but it is widely known that the Belgian represents Zidane's top summer target to replace Bale who has been struggling with injuries during his time in the Spanish capital.
Hazard has been at Chelsea since 2012 when he arrived from Lille and helped the Blues to win the Europa League in his first season.
"I think he is doing amazing, even in this last few months", added the 45-year-old, a winner of La Liga twice each with Real and Barca. But if there is a player you want, is available and he gives you value, I don't see it bad, but I don't have that. "It is not easy for players who play a bit less, maybe we ran out of gas".
In his incredible first two seasons at the Bernabeu, Zidane won one La Liga and two Champions League titles along with UEFA Super Cup and FIFA Club World Cup. "We have to find that positive energy and keep moving forward".
The champions currently trail leaders Barcelona by 16 points although they do have one game in hand.
Real Madrid legend Fernando Hierro has urged the club to stand by coach Zinedine Zidane.
Hazard, whose current deal runs out in 2020, recently gave supporters hope that he could sign a new deal after saying he was waiting for goalkeeper Thibaut Courtois to put pen to paper first.
How is Benzema? "I don't know".
This season has seen Los Blancos already lose three times in 17 games - Barca are unbeaten - which has been in stark contrast to a stellar 2017 which saw Madrid sweep up a record five trophies. "He will get back to scoring again".