The Daily Mail says Hazard is still on the Spanish giants shopping list despite failing to land him last summer.
But any move for the 27-year-old will depend on the future of the Welsh superstar who is struggling for game time at the Bernabeu.
The former Spurs attacker's relationship with Zinedine Zidane has deteriorated since he was overlooked for the Champions League first leg win over Paris Saint-Germain in February.
Zidane snubbed Bale in the return game in Paris and suffered the same fate in the quarter-final first leg against Juventus.
But underwhelming showings against Barcelona and Blue's second disastrous title defence have damaged Hazard's reputation in Spain, so leaving Zidane with a dilemma.
More pressing recruitment issues are a new goalkeeper and a striker to replace Karim Benzema.
That could leave Hazard watching Bale's situation closely as he ponders his future beyond the end of this season.