The Blues are keen to tie the Belgium playmaker down to a bumper new contract and Hazard has always insisted he is very happy at Stamford Bridge.
However, he has yet to commit his future and reports are rife suggesting the player is hoping Real come in and make him an offer to head to Spain.
Much will depend on the future of Real boss Zinedine Zidane and whether he stays in charge at the Bernabeu beyond the end of the season. If he does then and offer for Hazard is likely to go in at the end of the season as the Frenchman is a huge admirer of the Chelsea star and wants him on board.
Manchester City are also said to be keen on Hazard, but the player will want to head to Real if he does decide to push for a move away from Chelsea.
Meanwhile, reports are also refusing to go away regards the future of Thibaut Courtois, who is still said to be keen on a switch back to Madrid with Real.
Watford boss Javi Gracia does not think Abdoulaye Doucoure's form will be affected by his omission from France's latest squad.