Spanish outlet Diario Gol say the Liga giants have told Manchester United’s No.1 he remains on their wishlist despite talk of a move for Thibaut Courtois.
The Chelsea stopper is said to have instigated movements behind the scenes to engineer a transfer in the summer.
And those reports have apparently spooked De Gea who thought he was Real’s No.1 choice.
“I have never felt so good since I arrived in Chelsea”
Diario Gol claim Madrid president Florentino Perez has contacted De Gea to keep him updated on their interest.
However, they know it will be difficult to take United’s three-time player of the year away from Old Trafford.
And Perez has told the Spain international he will have to ask to leave if he wants to return home.
Despite Real’s supposed interest in Courtois, he has insisted he is loving life in London.
Earlier this week he said: “I have never felt so good since I arrived in Chelsea.
“On the field, I am good, I make the decisive stops when it is necessary.
“Sometimes I have just one or two to do. Against Hull, it was a little more at the weekend.
“But otherwise, I try to be ready to help the team. My game has improved a lot in the last two seasons.
“I sometimes have a few moments that are very difficult to manage but I’m doing well. I feel very confident right now.”