The Belgian goalkeeper has played on loan at Atletico from Chelsea since 2011 and reports in Spain have suggested he will cross the city to join Real when his Blues contract expires in 2016, or for a transfer fee in the next two years.
Courtois' father on Tuesday denied the speculation and following Atletico's subsequent 4-1 Champions League victory over AC Milan at the Vicente Calderon, the 21-year-old keeper broke his silence on the issue.
Speaking to AS, he said: "I've said it in three or four languages. Everyone knows these things have been said to destabilise the team.
"I have a deal with Atletico until June 30 and then two more years with Chelsea.
"I want to stay with them. It's okay if people follow my career, but I don't think they'll want to sell me.
"The press have put this about to destabilise us."
Atletico are currently second in the Primera Division table, three points behind city rivals Real, and will contest a Champions League quarter-final after convincingly overcoming Milan on Tuesday night.
"These kind of things often come out when there is an important game," Courtois added. "We know it's not true.
"Whatever came out in the press was not true and we are focused on the present. Today (Tuesday) was an example."