But the Blues are said to be aware that a summer sale may be their only option in the coming months.
Hazard has been heavily linked with a move to Madrid in recent seasons – and speculation has resurfaced since the return of Zinedine Zidane earlier this month.
And according to the Daily Record, the Frenchman’s club have already made an initial approach for the Chelsea star’s services.
Journalist Duncan Castles claims the Blues have rejected the proposal but are well aware that if Hazard opts to reject a new contract at Stamford Bridge, a sale may be their only option.
The 28-year-old has little over one year left to run on his current deal and has stalled on putting pen to paper recently.
Hazard has repeatedly flirted with a potential move to the Spanish capital and has praised Los Blancos on numerous occasions.
In other Chelsea news over the weekend:
Speaking last year, Hazard said: “Real Madrid is the best club in the world.
“I don’t want to lie, it is my dream since I was a kid.
“In my head, sometimes I wake up in the morning and think I want to go.
“Sometimes I think I want to stay. It is a hard decision. It is my future. I am 27 and I will turn 28 in January.
“It is also when you have a dream and you want to make it happen.
“It is like I have said a lot of times: if I leave I will be happy, I know if I stay I will be happy.”
Chelsea were beaten 2-0 by Everton on Sunday afternoon to lose yet more ground on the top four.
Maurizio Sarri is now once again under pressure at Stamford Bridge.