His current deal has 18 months left to run and the club also have an option to extend it by a further year, but club officials would be happy to hand him an extension on a deal worth £220,000-a-week to keep him beyond 2021.
The Spain global came close to moving to the Bernabeau in 2015 and has 18 months left on his current contract at Old Trafford.
Sir Alex Ferguson signed De Gea to replace Dutch legend Edwin van der Sar following the Spanish goalkeeper's impressive form for los Rojiblancos in La Liga and Europe.
The Independent: Senior figures at Madrid privately admit they are ready to let Gareth Bale leave in the summer.
According to The Independent, the Wales global could leave in the near future after growing isolated at the club due to his struggles with injuries and learning Spanish. It could have been a bleak night for Jose Mourinho and United, but for the heroics of the Spaniard was forced into eight saves, including one remarkable stop from a point-blank Luis Muriel header just before half-time that was so spectacular the Colombian striker congratulated United's number one as they left the field at the break.
The two giants need a win to boost their top four hopes and Merson has stressed the importance of the tie.
"When he first came, as players we were sitting there with doubts [about De Gea]", Ferdinand told BT Sport. Chelsea, meanwhile, go to Man City next, which will be hugely hard.