De Gea is understood to be torn between staying at Manchester United and returning to Spain.
In 2015, a proposed move to the Bernabeu collapsed late in the summer transfer window but Madrid's interest has remained.
But while Mourinho would be more than happy to retain De Gea at Old Trafford, it appears he is also open to selling him.
According to Spanish newspaper Marca, if United allow De Gea to leave, Mourinho wants at least £65million (75m euros) for him.
Manchester United stars celebrate Europa League win Fri, May 26, 2017
Click through the gallery for the best snaps of Jesse Lingard and Marcus Rashford enjoying Manchester after their Europa League victory
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Jesse Lingard and Marcus Rashford enjoy a night on the town after Man Utd's win
Real Madrid have remained interested in David de Gea
But if Morata, who has been unable to supplant Karim Benzema as Madrid's main striker, is included in the deal the fee wanted would be just £21.8m.
The report says Mourinho has a strong relationship with Morata having worked together at Madrid.
Alvaro Morata has had to play second fiddle to Karim Benzema
It is claimed a potential stumbling block in the deal could be Morata's preference to move to Serie A over the Premier League.
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And Madrid believe they can get as much as £65m for Morata.
Reports in Italy yesterday suggested Morata had agreed terms with AC Milan ahead of a £52m deal.