According to Het Laatste Nieuws (h/t Football Espana), with the goalkeeper's contract set to expire at the end of the 2018-19 campaign, some sides are taking an increased interest in his position. As well as Los Blancos, Juventus and Paris Saint-Germain are said to be monitoring Courtois' situation at Stamford Bridge.
As noted by Football Espana, Madrid have long been linked with a move for Manchester United's David De Gea, but a deal now appears unlikely; Athletic Bilbao youngster Kepa Arrizabalaga is said to be a target.
Meanwhile, other reports are cited that suggest the European champions are happy to keep faith with Keylor Navas and Kiko Casilla.
Courtois has been outstanding for the Blues since taking his place in the Chelsea first team in 2014. The 25-year-old has been between the sticks for two Premier League title wins, and in 2013-14 at Atletico Madrid, he was also a domestic champion.
Still, his future appears to be uncertain. HLN's Kristof Terreur noted the goalkeeper rejected the offer of an extension earlier in the year:
Losing the goalkeeper would be a massive blow to the Blues, although there'll be concerns creeping in with such a small amount of time remaining on his deal.
Courtois has established himself as one of the best goalkeepers in European football. After a tough 2015-16, he bounced back brilliantly the following season to help inspire Chelsea to the Premier League title. At his best, he's the type of presence that settles the defence in front of him down.
As noted by Matt Law of the Daily Telegraph, although he's still one of the younger members of the Chelsea squad, there have been burgeoning signs of leadership from Courtois:
The former Atletico man is a sensational shot stopper, utilising his rangy frame to claw efforts away from the corner of the goal.
There are other areas of his game that make Courtois so special, though. The 'keeper is commanding in coming off his line, regularly plucking loose crosses or long balls forward out of the air. His decision-making is positive, while he can be an intimidating presence in one-on-one situations with forwards.
He could potentially improve his distribution, as his play from the back does sometimes leave Chelsea fans on edge, per Liam Twomey of ESPN FC:
While Madrid have long been linked with a new goalkeeper, it would also make sense for Juve and PSG to pursue new stoppers in the summer.
Juventus will be without the legendary Gianluigi Buffon from the 2018-19 term, as he's set to retire from the game; Wojciech Szczesny has done well when given a chance, although doubts remain about whether he's up to the standard required. Meanwhile, the Ligue 1 side will feel they can upgrade on both Kevin Trapp and Alphonse Areola.
Chelsea supporters will be hopeful their starting stopper will eventually agree new terms, as things will get nervy if Courtois hasn't extended by the summer. While the Blues remain a major force in the game, it would be no surprise if the Belgian was tempted by the trio of options mentioned.