The 27-year-old has been increasingly linked with the Bernabeu club in the wake of their struggles to replace Cristiano Ronaldo, who moved to Juventus in the summer.
Meanwhile, Belgium ace Hazard has been in scintillating form since the beginning of the World Cup, where he helped Roberto Martinez’s side finish third, while he himself took the individual prize for finishing as the second-best individual player behind Croatia’s Luka Modric.
He has since followed it with equally strong displays in the Premier League, where he has fired Maurizio Sarri’s side joint top of the standings after eight matches by scoring seven goals and creating three more in the league.
Ahead of a Saturday clash against Manchester United, he has reiterated his commitment to the Stamford Bridge club.
“I can finish with Chelsea, no problem at all,” he told Sky Sports. “I am very happy with this club, with the team, my family is happy here.
“So, if I don’t go to Spain, it is not a problem. I love the fans – I think the fans love me! What happens in the future, I will be happy, so that’s it.”
Chelsea chairman Bruce Buck indicated earlier this week that the club “will do what it has to” in order to persuade the winger to remain with the Blues, though he hinted that Hazard, who is out of contract in 2020, may be tempted by an offer from Spain.
“Let’s see how it goes between now and the end of the season,” he said when asked about the prospect of the attacker penning a long-term deal.
Hazard has spent six years at Chelsea, having arrived from Lille for a fee of £31.5 million. He has played 310 times for the club, netting 97 goals in the process, while winning two Premier League titles and an FA Cup.
At the weekend, he is expected to lead Sarri’s side as they aim to open up a 10-point gap to Jose Mourinho’s struggling Manchester United team. Hazard has scored five times in his previous 13 games against the Old Trafford outfit.