Courtois was quoted saying his "heart is in Madrid" with his family now living there.
"If Real are really interested, my personal situation could influence things. The family aspect is priceless. But I repeat to you that, for the moment, I'm busy talking to Chelsea to extend," said the Belgian.
And Courtois' claims arrive after his agent, Christophe Henrotay, confirmed he was in regular contact with Real Madrid last summer.
"I meet regularly with the leaders of Real Madrid and the situation of Thibaut is evaluated. My role is to keep them informed of his situation," he told Sport/Voetbal magazine.
"Obviously Thibaut is interested in the big clubs and of course no least the last European champion. Courtois is a goalkeeper who makes you win matches, titles."