Manchester United star De Gea has been continually linked with Real Madrid ever since missing out on a move in 2015.
The Spain international came close to swapping Old Trafford for the Bernabeu, only for fax machine problems to scupper a deal.
Despite that, Real are keen to recruit him two years later with manager Zinedine Zidane desperate to succeed where his predecessor, Rafa Benitez, failed.
Express Sport understands United are making plans in case their star asset does depart, with Inter Milan's Samir Handanovic on their radar.
However, reports in Spain are suggesting that Jose Mourinho could be about to win one of the transfer battles of the summer.
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Diario Gol say that De Gea has told Real he will stay at United for the long haul unless they sell Keylor Navas and wrap up a deal quickly.
The 26-year-old was reportedly fuming after missing out on his dream move two years ago, with Madrid waiting until transfer deadline day to make a first bid.
As a result, he is not prepared to wait all summer for his future to be clarified.
The report adds that Real are not willing to meet United's lofty asking price for the star.
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David De Gea could renew his contract at Manchester United despite Real Madrid's interest
It is said that Zidane tabled an offer of just £43million for him, while United want a fee in the region of £63m.
United boss Mourinho said earlier this month that he was determined to stop his No1 leaving for the newly-crowned La Liga champions.
"David? I think the first match against LA Galaxy in pre-season in Los Angeles," Mourinho told Sky Sports after their goalless draw with Southampton.
"David is top of the world and we want to keep top of the world."