The Spanish side have an opening offer ready to be submitted as they look to bring the 26-year-old goalkeeper - winner of the Golden Glove for his performances at the World Cup in Russia - back to Madrid.
However, Los Blancos first have to wait until Chelsea reach an agreement for Courtois' successor at Stamford Bridge, something which is still far away from competition.
Both Real Madrid and Chelsea have been eager to sign a new goalkeeper this summer but they failed in their attempts to land Alisson Becker, who instead chose to join Liverpool, while the former also failed to complete a deal for Kepa Arrizabalaga.
Marca claim that although Courtois will remain on holiday, the Belgium international is entering the most decisive week of the entire transfer.
Hopes in Real Madrid's camp are that he will link up with the squad when the travel to America in pre-season, or at the latest in time for their European Super Cup.
Courtois has spent seven years on the books with Chelsea, but his career in west London didn't kick off until a three-year loan spell with Atlético Madrid came to an end in 2014. He has since gone on to make 154 appearances for the Blues across all competitions, keeping 58 clean sheets.