De Gea has been at Manchester United since signing from Atletico Madrid in 2011.
During his time at Old Trafford he has been one of their standout players, winning the club's player of the year award for each of the past three years.
He came close to joining Real Madrid in 2015 only for a faulty fax machine to scupper a deal.
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David De Gea's girlfriend Edurne wants him to move to Real Madrid
David De Gea has been in fine form for Manchester United this season
The Spain international continues to be linked with a move to the Spanish capital, however, with Madrid eager to replace Keylor Navas.
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And Spanish outlet Diario Gol has claimed the goalkeeper's girlfriend Edurne is house-hunting in Madrid ahead of a potential summer transfer.
Edurne and De Gea spend much time apart due to her career as a singer.
David De Gea has been at Manchester United since 2011
It is said they want to start a family together and both of them want that to be in the Spanish capital.
Edurne is looking at the area of La Finca, where Cristiano Ronaldo, Gareth Bale and Toni Kroos currently live.
Should United lose De Gea, then they could make a move for AC Milan star Gianluigi Donnarumma.
The 18-year-old is hot property across Europe's top clubs and his agent Mino Raiola could use his United connections to ensure his client move to Old Trafford.