Reports in Spain have claimed the goalkeeper has told Jose Mourinho he wants a switch to the Bernabeu.
"Do Real Madrid want De Gea? You bet they do," Spanish expert Guillem Balague wrote for Sky Sports.
“What surprises me, however, is why a club like Manchester United - that have no need to sell him - would be prepared to let him leave. I'm sensing a hidden agenda.
“Just why would he want to leave a club that is one of the world's biggest, a club on the up, and where he is unquestionably the number one to move to Madrid where he will be on less money and the pressure will be higher?
“Not for the first time in situations like this, the Spanish press have announced that not only does De Gea want to leave but have gone as far as to say that he has even requested a move.
“I have been told that he has not said anything of the kind to United. Why do the Spanish press keeps insisting he wants to go then?"