The Blues are fighting to keep hold of their top personnel with Real ready to may mammoth sums to swoop.
Hazard's time at Chelsea appears to be coming to an end after the Belgium star openly courted a move away from Stamford Bridge.
The forward was one of the top performers at this summer's World Cup but he would not be playing Champions League football next season if he was to remain at Chelsea.
Real Madrid are desperate to find a replacement for Cristiano Ronaldo , who moved to Juventus for close to £100million last week.
And reports are now suggesting that the European champions may have a major breakthrough in their search for their next superstar.
Hazard's time at Chelsea appears to be coming to an end
Le10Sport are claiming that Chelsea and Real have come to an agreement on a £190million move.
They claim in the report, however, that the figure may also include the fee for Thibaut Courtois, who is also linked with a move away from the London club.
Elsewhere, French outlet RMC Sport say an agreement on personal terms has been reached between Hazard and Real.
Hazard still has two years left on his Blues contract - but his market value will fall drastically if he does not agree a new contract in west London.
Hazard was one of Belgium's star men at the World Cup
Courtois is also linked with a move to Real Madrid
After Belgium's win against England in the World Cup third-place playoff, Hazard admitted he was considering leaving Chelsea.
"After six wonderful years at Chelsea it might be time to discover something different," he said.
"Certainly after this World Cup. I can decide if I want to stay or go, but Chelsea will make the final decision – if they want to let me go. You know my preferred destination."
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