The Premier League champions have opened talks with the Belgian playmaker and are ready to pay him £320,000 a week to snub a switch to Spain.
Hazard was hugely influential in helping Antonio Conte’s side win the their second Premier League title in the last three seasons.
He still has three years left to run on his current £200,000-a-week deal but the club are ready to dig deep to ensure he is still playing in West London at the start of next season.
The highest earning Premier League star is the world’s costliest player Paul Pogba who is paid around £290,000 a week by Manchester United.
Chelsea want to make Eden Hazard the highest paid player in the Premier League
Zinedine Zidane has long been an admirer of Eden Hazard
Chelsea are set to offer Eden Hazard a new contract worth £320,000-a-week
Hazard isn’t even the highest paid player at Chelsea with Cesc Fabregas understood to be on around £220,000 despite not even being the first name on Conte’s team sheet.
Chelsea are taking the threat from Real to their most prized asset seriously after it emerged they have had three meetings with his representatives in London.
But the Blues are not only willing to give him parity with the best paid players in the Premier League but eclipse them to keep Hazard happy.
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Hazard will still be someway short of the two highest paid players in the world. His former Chelsea team mate Oscar earns around £400,000 a week from Shanghai SIPG.
While another Chinese Super League side Shanghai Shenua are splashing out £615,000 a week on Carlos Tevez.
The Belgium international dropped his biggest hint yet that he will remain at Chelsea in a recent interview.
Eden Hazard recently suggested he wants to remain at Chelsea for a couple of years
"I'm good here," Hazard told Singapore outlet The Strait Times.
"I'm at one of the best clubs in the world and I think I'm gonna stay for a couple of years.
"I'm very happy. You can see on the pitch that I'm happy.
"Next season we will have the Champions League to play but we want to keep the Premier League trophy in Chelsea."