According to Carlos Carpio of Marca, Thierry Hazard reached out to the European champions to offer clarity over the Belgium international's future, putting Hazard's position in London under further scrutiny.
"[Thierry] explained that talks over a new deal at Stamford Bridge were on hold because Eden thinks the time has come to move on with no Champions League football in west London next season," Carpio said.
It's added that there is interest in the player from Madrid's perspective, with the club said to view the Chelsea man as a possible alternative to Paris Saint-Germain's Neymar in the transfer window this summer.
Carpio said Hazard is "looking for a style of football that suits him and a coach who will try to exploit his talents after growing frustrated under Jose Mourinho and Antonio Conte."
Given Hazard only has until 2020 to run on his current Chelsea contract, Blues supporters will be getting increasingly concerned about keeping hold of their star man, especially if there is serious interest from Madrid.
As noted by Kristof Terreur of Het Laatste Nieuws, the forward was the standout attacker for the Blues in what was a testing campaign:
Hazard did have lulls during the 2017-18 season, too, although Chelsea consistently looked to him in the final third.
Whether playing from the flanks or through the middle, the Belgium star is a threat. Hazard is almost impossible to get the ball from, as he can wriggle away from defenders and burst into space with his change of pace.
The forward is showing his class on the big stage at the moment, as he's shone for Belgium at the FIFA World Cup in Russia.
He already has two goals, and as noted by Ian Ladyman of the Daily Mail, Hazard appears to be in top gear:
If Madrid were able to get him then it would be a massive boost, as Hazard would add something different to their attack. The prospect of him linking up with someone like Cristiano Ronaldo is a tantalising one.
Journalist Ste Hoare said a positive World Cup may just convince Real to make a big effort to secure the Chelsea man:
The Blues are in a tough position. At the moment the club feels in a state of flux, with Antonio Conte still in charge despite persistent rumours about Maurizio Sarri taking over as boss, per Neil McLeman of the Daily Mirror.
That uncertainty and the lack of Champions League football at Chelsea next season make it less likely Hazard will want to stick around next term. If Madrid do decide to test the resolve of the Blues with a huge offer, then the Premier League outfit would have a massive decision to make.