Courtois, whose current deal runs out in 2019, has been the subject of links with the Champions League holders amid uncertainty over his future at Stamford Bridge.
According to Spanish source Don Balon, Courtois is expected to begin negotiations with Madrid once the Belgian receives the green light from Zidane.
The report adds that Madrid's failed move for Athletic Bilbao goalkeeper Kepa Arrizabalaga has made Courtois a priority signing for Los Blancos in the January transfer window.
The 25-year-old has previously admitted that his family, who live in Spain, are a considerable factor in his future position in West London.
Courtois spent successive seasons in the country on loan from the Blues at Atletico Madrid before cementing a place in Chelsea's first team.