Hazard could move back to England after keeping hold of his Surrey house, according to the Athletic.
And the winger, 30, previously refused to rule out a return to Chelsea as talk of a stunning transfer comeback hots up.
Insiders suggest the Hazard family still own the pad they lived in near the Blues' Cobham training ground.
He said: "When I finish here I'll come back."
It is unclear whether that would be as a Chelsea player or simply to live in England after his playing career.
But after criticism rained down on him after joking with Chelsea players after Real's Champions League defeat on Wednesday night, there's local demands that Hazard be sold this summer.