The Evening Standard is reporting that los Blancos are weighing up a potential offer for the Belgium international at the end of the current campaign.
Hazard made a strong start to the 2017-18 season but the 27-year-old has struggled in the second half of the campaign like most of his Chelsea FC team-mates.
The same article states that Real Madrid haven’t made contact with the defending Premier League champions or Hazard’s representatives about a potential summer move.
According to the same story, Real Madrid could be reluctant to match Chelsea FC’s £100m asking price given Marcos Asensio is a similar talent with a big future at the age of 22.
Chelsea FC are reported to be in negotiations with Hazard over a new deal as the Belgian star looks to increase his wages from £200,000 a week to £300,000 a week.
Hazard has scored 11 times and has made three assists in 27 appearances in the Premier League this term.
The Blues have won the Premier League title in two of the past three seasons but Chelsea FC are eight points adrift of fourth-placed Tottenham Hotspur.
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