The Blues talisman is a long-time Real Madrid target, and suggested earlier this summer that his future lay away from West London.
Spanish clubs are still able to sign players until August 31. Barcelona have also been linked with the Belgium World Cup star.
But Hazard has now dashed the La Liga giants' hopes of signing him by pledging his future to Maurizio Sarri's side.
The playmaker, 27, is in his seventh season at Chelsea. He came on as a sub to set up Marcos Alonso's winner as the Blues beat Arsenal 3-2 to extend their 100 per cent start to the campaign.
Hazard told French broadcaster RMC: "I am happy at Chelsea for now. I have two years left on my contract, and we will see what happens.
"Leave this year? I won't go. The transfer window in England is already closed.
"Players can leave, but clubs can't make new signings.
"It would be strange for Chelsea's people to let me go without signing anyone to replace me.
"You could see once again in the Arsenal game that the fans love me, and I am happy here.
"We will see what happens in a year or two's time.
"You know what I said after the World Cup finals. I am happy at Chelsea and I don't yet want to talk about leaving.
"Plenty of things have been said about me – a lot of rubbish and everything."
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