The 27-year-old has been linked with a move to the Bernabeu ever since his transfer to the Spanish and European champions collapsed in August 2015.
De Gea's current contract expires in June 2019, but the Old Trafford club have the option extend his deal by a further year.
It is understood that Jose Mourinho is open to selling the highly-rated stopper, but only if he gets a player in return.
Gareth Bale is a name that has consistently been linked with United over the last couple of years, while Mourinho is also keen to link up with defender Raphael Varane again.
Is there a swap deal on the cards? Let us know what you think in the comments.