The Sun newspaper says Real have come to the realisation that a deal to bring Spain international De Gea to the Santiago Bernabeu would be too difficult to complete.
As a result, the 11-time European champions have switched their attention to the 24-year-old Courtois, who reportedly wishes to return to Spain.
The Belgium goalkeeper spent three years on loan at Atletico Madrid and his family still resides in the city.
Spanish radio station claimed earlier this week that Courtois was desperate to move to Real in the summer that he expects the Madrid club to make a bid for him.
Speaking in November, Courtois denied that he had ever spoken to Real about a potential transfer and insisted that he was happy at Chelsea.
"At Chelsea everything is going well. It's is a great club. There is no reason not to be happy at Chelsea. You never know what will happen in the future but this doesn't mean that I am not happy here. At the moment I am very well, in a very good atmosphere and that makes me happier at home too," the 24-year-old said.
"I never said that I wanted to leave Chelsea. I have a contract until 2019. At the end of the season we can talk, I guess Chelsea will do it because they trust in me, they see that I am good, that I am helping the team," he said.
"I never had anything with Real Madrid. I did not see anything published but I never had any contact with Real Madrid."
Real came close to signing De Gea from United in 2015 but the transfer collapsed because the necessary paperwork was not filed in time.