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The Belgium international joined 'Los Blancos' in 2019 but has yet to win fans over after a string of injuries.
He's currently nursing a hamstring problem but Spanish publication AS per Sport Witness claim his name has been 'ringing around London' in the last few days.
Hazard won the Premier League twice with Chelsea as well as the Europa League during a seven year stint.
Despite those happy memories, a move looks to be out of reach as Madrid would require a fee of around €60 million.
Madrid paid €100 million for Hazard and are spreading that out in instalments over five years.
The fee is considered to be 'very high' by the Blues and they're aware of Hazard's recent performances.
Thomas Tuchel guided Chelsea to the Champions League last season and believes he has enough cover on the wings.
He'd rather spend money on a striker after using Kai Havertz as a false nine for most of his tenure in charge.
Chelsea had been chasing Borussia Dortmund starlet Erling Haaland and prepared offers including some of their own players.
He'll likely be staying with Dortmund however and Chelsea have turned their attentions elsewhere - specifically, Robert Lewandowski.
Further reports are also suggesting Chelsea have been discussing Lewandowski's future with his agent Pini Zahavi.
Tuchel told reporters at the end of last season per Evening Standard: "Two or three could be very, very good.
"It's a constant thing to never deny change. That you always bring new energy, new guys who question the old beliefs, who challenge everybody in the training and in matches, so I think it's a good thing.
"We don't need another seven and another complete turnover because it's also our job to keep on improving, because we have still a young squad and it's not about stealing from them the chance to prove it again that they are capable of growing and evolving.
"But we have some ideas, of course, to make the group stronger and I think this can always be a positive thing to challenge all of us."
Featured Image Credit: PA Images
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