The Belgium international is now into the final 12 months of his Blues deal and reportedly has no intention of agreeing fresh terms.
Madrid are long-term admirers of the 26-year-old, but they are said to have been unsuccessful with their only previous approach and may now look elsewhere for a new number one.
Following the conclusion of Belgium's World Cup campaign, Courtois will spend time contemplating his future, but admits that the ball remains firmly in Chelsea's court.
"Now I'm going to talk to my agent to see what the possibilities are," he said after the 2-0 third-place playoff win against England. "All options are open for me. I may also stay at Chelsea.
"People always complain that players don't comply with their contracts, but maybe they do. I don't think they will keep someone with my qualities on the bench, even if I don't sign [a new contract]. But maybe [staying] is possible, because I like it in London."
Asked if he could rule out a move to Madrid this summer or beyond, the keeper replied: "No".
Courtois revealed at the end of last year that he is attracted to the Spanish capital because that is where his children are being raised, having previously spent three years with Atletico Madrid.