The winger, who was named PFA Player of the Year for his splendid form last season, has struggled this campaign with goals and assists continually eluding him.
Despite that, the La Liga giants are said to be undeterred and could move for him given the uncertainty surrounding the future of talisman Cristiano Ronaldo and Colmbian star James Rodriguez.
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Last season Hazard was the best player in the Premier League, with his contribution key in the Blues ending their four-year wait for the Premier League crown.
There was also evidence of his world class quality when representing the club in the Champions League, though his goal in the Blues’ 2-2 draw with Ligue 1 side Paris Saint-Germain in the round of 16 was not enough to save them from being eliminated from the competition.
This term things have been less straightforward, and the Blues’ slump - that sees them lie in the bottom half of the league table - has prompted many to criticise their no. 10 for the shambolic nature of his performances.
Others who were crucial in the club’s successful title assault last season have also struggled, with Diego Costa, Cesc Fabregas and John Terry all looking different propositions compared to this time last year.
Madrid are a club in crisis and, regardless of whether or not Rafa Benitez remains at the club beyond the end of the season, are keen to land a marquee name to compete with Barcelona.
Ronaldo remains a superstar, but some of his performances have hinted at a magician whose powers are on the wane and, with Paris Saint-Germain and Manchester United interested, he may be in his last season in the Spanish capital.
Madrid have proven in the past that regardless of their performances on the pitch they are a club whose appeal is stronger than no other, with their unique lure allowing them to land Gareth Bale, Rodriguez and Luka Modric in recent years.
Hazard would not be short of admirers if he were to leave the capital but the Spanish giants would be confident of winning any race for his signature.
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