Real are wasting little time in preparing for next season after rehiring Zinedine Zidane this week and have already secured the €50m signing of Brazilian defender Eder Militao from Porto.
According to The Sun, representatives from Madrid have already visited London for talks and an opening offer of £70m will be the start of their statement of intent to sign Hazard.
The tabloid newspaper claims that Real are aware Chelsea will reject that figure, but this will be the mark to kick off what could turn into one of the summers most fraught transfer sagas. A figure of £100m has often previously been thrown around on the subject of Hazards future.
Chelsea manager Maurizio Sarri had already claimed this week that he is not worried about the prospect of Hazard joining Real as he only wants players who want to be at Stamford Bridge.
You have to ask to Hazard (about Zidane) I think. I dont know at the moment. I didnt speak with Eden about Zidane," Sarri said on the matter.
"I am not worried because you know my opinion. I want only in my team players who want to play for Chelsea, so I cant be worried."
Hazard is known to idolise Zidane after admiring the Frenchman during his playing days. The rumours of a switch to Madrid died down a little after Zidane unexpectedly resigned last May, only to reignite in a big way when he was surprisingly reappointed.
Hazard was left on the bench on Thursday night as Chelsea thrashed Dynamo Kyiv 5-0 in Ukraine, booking their place in the Europa League quarter finals with an 8-0 aggregate win.