The Belgian won the PFA Player of the Year and Football Writers' Association Footballer of the Year awards for his efforts last season after racking up 19 goals and 13 assists in all competitions and helping Chelsea romp to the Premier League title.
Squawka Football share more of the 24-year-old's impressive stats:
Typically considered one of the world's best, the attacking midfielder would indeed be a good fit at the Bernabeu thanks to his enormous profile, though Real have little need for him with stars like Gareth Bale, James Rodriguez and Isco already on their roster.
Chelsea would undoubtedly be reluctant to part with their star, though, so Perez might have to offer another world-record fee to prise him away from the Premier League, as he did with Bale and Cristiano Ronaldo before him. But Castles notes he "will not baulk" at doing so.
However, for Hazard to warrant such a hefty fee, he will need to markedly improve his performances for Chelsea.
Like the rest of his team, Hazard has struggled greatly this season not only to meet the standards set last year, but to even come close.
Squawka Football revealed his lengthy goal drought prior to his strike against Arsenal and captured his abject first-half performance against Maccabi Tel Aviv, which was symptomatic of his campaign thus far:
Football writer Liam Canning is one of many who have been critical of his ineffective displays:
Of course, like the Blues, Hazard will almost inevitably return to form sooner or later thanks to his incredible quality. Still, if he fails to turn things around soon, Perez might rethink his pursuit of the midfielder, which could lead to the creation of a frustrating catch-22 for Chelsea.
Ultimately, though, they need him to recapture his earlier form, as a title challenge seems incredibly unlikely otherwise, and it's far from guaranteed he'll jump ship at the first offer Madrid throw his way.
Chelsea Look to Giorgi Loria to Solve Goalkeeping Troubles
According to Uche Amako of the Express, Marca reported that Chelsea are eyeing a move for Georgia international Giorgi Loria, possibly on an emergency loan to cover for Thibaut Courtois, who is set for a lengthy layoff due to a knee injury.
Georgia manager Kakhaber Tskhadadze told the Georgian media, per Marca: "There were two days where Chelsea would not stop calling."
The 29-year-old, currently plying his trade in Russia, spent much of his career at Dinamo Tbilisi, where he kept 57 clean sheets in 136 league matches, according to Transfermarkt.
The link is a strange one, as the Blues have an able stopper filling in for Courtois already—Asmir Begovic.
Begovic may not quite be of Courtois' quality or on the same level as Petr Cech, who left for Arsenal in the summer, but the Bosnian is an experienced Premier League 'keeper who is more than capable of carrying them over.
Though he has conceded 10 goals in six appearances this season, it is Chelsea's defenders who have been principally to blame.
Because of Begovic's presence, Chelsea aren't likely to pursue another goalkeeper before Courtois returns.
If they do, it would surely be for someone far more proven at the highest level than Loria.