The Belgium international is a long-term target for the Spanish giants.
The winger almost joined Real last summer, however, Hazard broke his ankle, ending any hope of a deal.
Hazard, 27, issued a come-and-get-me plea to Real following Belgium’s World Cup third-place playoff victory against England last weekend.
And according to RMC Sport, Hazard has a verbal agreement with Real to join this summer.
However, they reckon both Real and Chelsea are yet to agree on a deal for the Stamford Bridge superstar.
Real are desperate for Hazard to replace Cristiano Ronaldo at the Bernabeu – and the Chelsea forward fancies a move to La Liga.
Speaking about his Chelsea future last weekend, Hazard said: “After six wonderful years at Chelsea, it might be time to discover something different.
“I can decide if I want to stay or go, but Chelsea will make the final decision – if they want to let me go.
“For my career, certainly after this World Cup, I’m at a moment where I might change.
“We all know that I’ve always felt well at Chelsea, and I’ve been linked to all the big clubs.
“Next week it will be Bayern (Munich). No, I’m joking. You all know my preferred destination.”
Barcelona have also been reported to be interested in the Chelsea man.