The Red Devils star is a long-term target for the Spanish giants.
De Gea, 26, nearly joined the La Liga champions in 2015 but a late fax ended any hope of a move.
Reports have suggested Real will return for the Spain international with club president Florentino Perez desperate to land the goalkeeper.
And Spanish transfer outlet Don Balon say De Gea is refusing to miss out on the chance to join Real this summer.
They reckon the Spain stopper has told his agent Mendes to sort the move and the super agent is working with Bernabeu chiefs.
Jose Mourinho is desperate to keep hold of De Gea this summer.
The United boss wants to mount a Premier League title charge and challenge for the Champions League next campaign.
Mourinho has already landed Romelu Lukaku and Victor Lindelof this summer for around £105m.
And the Special One has other targets, including Inter Milan ace Ivan Perisic.
