Hazard has publicly stated that he will not rule out a move away from Stamford Bridge unless the uncertainty over their managerial situation is resolved, with Maurizio Sarri still expected to take charge despite Antonio Conte taking pre-season training so far.
Hazard is understood to be seen as a potential replacement for Cristiano Ronaldo at the Bernabeu, but Sport reports that the European champions could face competition for his signature from their bitter Clasico rivals.
Barcelona are reportedly ready to make a £100m bid for the 27-year-old, having cooled their interest in Tottenham Hotspur's Christian Eriksen in order to focus on Hazard.
Hazard is currently at the World Cup with Belgium, where he will contest the third-place playoff against England on Saturday.
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Where will Eden Hazard be playing his football next season?