Hazard enjoyed an excellent season for Chelsea as they won the Premier League title but speculation surrounding a move to Madrid, who have been long-term admirers of the Belgian star, has refused to disappear.
Express Sport understands Chelsea are prepared to make Hazard the highest paid player in Premier League history in order to prevent a move to Spain.
But the 26-year-old has now revealed he would consider joining the Champions League winners, which raises fresh doubts about his Stamford Bridge future.
"Of course, I would consider it if Madrid made an offer," Hazard said.
Chelsea summer transfer targets Sat, June 3, 2017
Who could Chelsea sign this summer?
Play slideshow Bongarts/Getty Images 1 of 12
Of course, I would consider it if Madrid made an offer
"I am keen to win trophies.
"It would be great to win the Champions League. But Chelsea's goal is to win the Champions League as well. Honestly, I do not know what will happen.
"I only know that I still have a contract with Chelsea for three seasons and that we just had an amazing 2016-17 campaign. We want to continue on this path and want to build on this in the Champions League.
Eden Hazard says he would consider a move to Real Madrid
Get Quotes on Home Insurance
Eden Hazard is currently on international duty with Belgium
"I am feeling very well at Chelsea. But you never know what will happen.
"I have not met with the board yet to discuss a new deal. I have two games with Belgium coming up first and I am off on my holiday after that. I want to think about football as little as possible."
Hazard, who still has three years left on his Chelsea contract, was speaking ahead of Belgium’s friendly against Czech Republic on Monday night.