It is thought Courtois will be allowed to leave the club this summer, with Madrid his preferred destination, but Chelsea has yet to make progress on a deal to sign a new keeper, Sky Sports reported.
SSN reported last week that Jordan Pickford was Chelsea’s number one target, but the England international is set for contract talks at Everton when he returns to the club this summer.
Courtois, who has one year left on his current Chelsea deal, is valued at £32 million by Madrid and it is expected that there would be no issue with agreeing personal terms.
But, the Belgium keeper will start the new season at Stamford Bridge if no successor can be found before deadline day and could then run down his current deal, meaning he would be able to leave for free next summer.
Courtois could yet sign a new contract at Chelsea and has previously said that "all options are open".
New Chelsea boss Maurizio Sarri has told reporters he wants to talk directly to Courtois to gauge how the 26-year-old is feeling before making any decision about his future.
Chelsea has already signed Rob Green on a one-year deal, but the 38-year-old is expected to act as third choice.