Belgium international Courtois spent three seasons on loan with Madrid's fierce rivals Atletico before establishing himself as Chelsea number one for the 2014-15 Premier League season.
Madrid are thought to be on the lookout for a goalkeeping upgrade on the back of their 2015 move for Manchester United's David de Gea falling through and Keylor Navas' dwindling form this term.
By contrast, Courtois has cut an assured figure in helping to steer Chelsea towards Premier League glory and foresees his long-term future being at Stamford Bridge.
"I don't see myself at Real Madrid," he told Cadena Ser.
"I see myself at Chelsea, the club that six years ago saw me playing in Belgium and gave me the opportunity to sign for them.
"They also allowed me to be three years at Atletico, which helped me to be the keeper that I am now.
"I feel that I'm key to the team, I'm very happy at Chelsea, and I don't see myself anywhere else."
Courtois' current Chelsea deal expires in 2019 and, although talks over an extension are yet to take place, the factor of his family remaining based in Madrid appears unlikely to draw him away from the English capital.
"For the time being, we have not spoken about a contract extension. We are focusing on the league," he said.
"We will see at the end of the season if they offer me something. For the time being, there has not been an offer.
"I'm happy in London and I'm delighted with the success we are having this season.
"I owe a lot to Spain and I go often there to visit the family, who are in Madrid. But I'm happy in London."
Antonio Conte's Chelsea are in a dominant position in the Premier League, 10 points clear of nearest challengers Tottenham with as many games to play.
"We are working well with Conte," Courtois added.
"I see that there is a long-term project to win trophies, not just domestically but also in Europe. There is a lot of ambition to play in the Champions League next season."