The Spanish capital club do have one factor on their side, however, with Hazard's contract set to enter its final year this summer.
That's what they did this summer, sending Mateo Kovacic on loan to Stamford Bridge to sweeten the deal to bring in Thibaut Courtois at the eleventh hour - and they apparently want to repeat the trick again.
Richarlison is now in his second season in England, having made his way to Watford from Fluminense in the summer of 2017.
The Brazil global has scored 10 Premier League goals this season for his new club but overall the team have struggled under Marco Silva. The two options on the table are a new Chelsea deal or a transfer to Real Madrid.
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The Blues are now in a precarious situation, with widespread reports linking Eden Hazard with a move away from Stamford Bridge.
The 28-year-old has also made no secret of his desire to play for Real Madrid. "I have made a decision". "I have decided", said the 28-year-old Belgian global. "He has the potential to be the best player in Europe at the moment", said Maurizio Sarri last week.
The problem though, is that Brazilian forward has been quite inconsistent for both Everton and Watford, although his in-form periods have been more outstretched at his current club, which is a positive. It's for that reason that when Chelsea post things like this on Instagram we're inclined to get a little excited.
Hazard has frequently stated his dream of playing for Real Madrid in recent years while the La Liga giants have long considered the Belgian worldwide a potential big-money signing.