De Gea has been at Manchester United since signing from Atletico Madrid in 2011, establishing himself as one of the best goalkeepers in the world.
However, he nearly left in the summer of 2015 when Real Madrid came calling.
The Spain international was desperate to secure a move to the Bernabeu, but a faulty fax machine ultimately saw him remain at Old Trafford.
Yet Spanish website Diarrio Gol claims that Real Madrid now think he is unhappy, with his contract situation the reason why.
When his move to Real collapsed two years ago, the player went on to sign a contract extension.
Manchester United ace David De Gea snapped out in Hale
Thu, October 12, 2017
David De Gea looked relaxed as he was snapped out in Hale village today
Eamonn and James Clarke
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David De Gea snapped out in Hale village
That means his current deal expires in 2019 and, at present, the club are yet to agree a renewal.
And Diario Gol say that De Gea is unhappy with the offer that Mourinho has currently presented him.
He supposedly wants a salary in keeping with his status as one of the club's best players, similar to what the likes of Romelu Lukaku and Paul Pogba currently pocket each week.
But so far, the Red Devils have resisted the urge to bow to his demands.
This news has reached the ears of Real Madrid president Florentino Perez.
Man Utd News: Real Madrid think David De Gea is angry at Jose Mourinho
Man Utd News: Real Madrid nearly signed David De Gea but he signed a new deal instead
Perez still harbours hope of landing the 26-year-old, particularly given Keylor Navas' inconsistent form.
But United are likely to prove tough negotiators – especially with the two clubs' relationship already strained.
Real refused to let the Red Devils sign Alvaro Morata, who ended up joining Chelsea instead.
And Los Blancos were also unwilling to let Gareth Bale return to the Premier League.