New Chelsea boss Maurizio Sarri is adamant that the club will resist any offers for Hazard before the European transfer window closes.
But Real’s power-brokers are desperate for Hazard to replace superstar Cristiano Ronaldo, who left for Juventus last month.
Now Real are set to up their £150m valuation closer to the £200m that Chelsea have placed on his head.
Hazard – who is stalling on signing a new £300,000 a week deal – is not openly pushing to leave and has spoken to boss Sarri since returning from his break after the World Cup.
“Hazard has congratulated me on signing for Real Madrid,” said Belgian goalkeeper.
“He is a great player and I would like to be always at his side, let’s see what happens in the future.
“If he can come [to Real Madrid], it would be fantastic.”
But Sarri is adamant that Hazard is happy to remain at Stamford Bridge.
“Hazard is with us,” Sarri told reporters.
“It is not a problem, I have spoken with his three or four times.
“He never said anything about the market.
But Real’s top brass will meet this week with a view to making one last big money bid to lure Hazard to Spain before the August 31 deadline.
As for the Blues, they started their Premier League campaign with a convincing 3-0 win over Huddersfield on Saturday.
Goals from N’Golo Kante, Jorginho and Pedro were enough to silence the Terriers at the John Smith’s Stadium.
Chelsea transfer news Maurizio Sarri
Chelsea transfer news: Maurizio Sarri’s Blues beat Huddersfield on Saturday (Image: GETTY)
But despite the margin of victory Sarri concedes the Chelsea players are still not playing at the level he wants them to be.
“The game was more difficult than the result,” he said. “If you see the result you think it was a very easy match but in the first half it was very difficult against physical opponents.
“We are not a physical team so for 20 minutes we were in trouble but we did very well.
“In this moment we are not at the top of our potential but we had the capacity to suffer for 20 minutes in the first half.”