Courtois is entering the final year of his contract at Chelsea and has so far offered no indication that he will extend his stay at Stamford Bridge.
Chelsea are therefore willing to cash in on the 26-year-old rather than lose him on a free transfer next summer, and Spanish publication Marca reports that Madrid are already in advanced talks for the Belgium international.
A deal could reportedly be announced in the coming days, with the two clubs thought to have agreed a fee of around £31m.
Courtois, who won the Golden Gloves for his performances at this summer’s World Cup, has made no secret of his desire to return to Madrid at some point, having spent three years in the city with Atletico Madrid earlier in his career.
Chelsea have been linked with a move for Roma and Brazil goalkeeper Alisson Becker as a replacement for Courtois, although they are expected to face competition from Liverpool for his services.