The Spaniard has been continually linked with a transfer to Los Blancos, after a failed move to the Bernabeu back in 2015.
De Gea had expected to return home in the summer transfer window, ahead of the 2015/16 season, but Manchester United alleged submitted the paperwork to complete the deal too late.
Los Blancos were frustrated in missing out on their man, but have stayed hot on his heels, and were strongly linked with a move for him ahead of the current season.
The Spaniard, who was born in Madrid and previously represented Atletico, has been widely tipped to return to the Spanish capital at the end of the season.
But he gave Manchester United hope that he would be willing to stay at the Old Trafford club in a recent interview.
Speaking to El Confidencial, the shot-stopper said: “Real Madrid? I’m the goalkeeper of Manchester United and Spain. What more could I ask for?”
Sir Alex Ferguson parted with nearly £20million – the second biggest fee spent on a goalkeeper – to land De Gea on a five-year deal back in 2011.