Hazard last week told a Belgium television station that it was his dream to play under Zidane and Real have interpreted it as a come and get me plea.
The 26 year-old has helped The Blues to win two Premier League titles since moving to West London five years ago but his days at the club could be numbered .
And Chelsea had been hoping that he would agree to put pen to paper on a new contract and were willing to make him the highest paid player in the Premier League.
But talks about the £300,000 a week contract have been dragging on without any agreement and Real are ready to seize their chance to make a move.
Real tried to sign Hazard last summer only for the move to be blocked by Real President Florentino Perez who now appears to have had a change of heart.
Perez is ready to go all out to take Hazard to the Spanish capital even though Chelsea would be reluctant sellers as he is a player who would be impossible to replace.
Hazard spoke about his dream to play under Zinedine Zidane earlier this month.
He said: ”I do not know what will happen in my career in the future. However, for sure, to play under Zidane would be a dream.
“I am enjoying life at Chelsea. I still have a lot of things to achieve with them. I am focused on playing for Chelsea.”