Real Madrid president Florentino Perez is determined to sign De Gea, two years after missing out on the Manchester United star.
The Spain international nearly moved to the Bernabeu in 2015, only for a faulty fax machine to scupper the deal.
De Gea then went on to sign a new contract with the club but, less than two years after doing that, Real are likely to make a bid to lure him back to his homeland again this summer.
Express Sport understands United are keeping tabs on Inter Milan's Samir Handanovic in case their star asset leaves for the Bernabeu.
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Manchester United star David De Gea is wanted by Real Madrid
Real Madrid players do not want Manchester United star David De Gea to join this summer
However, Spanish outlet Diario Gol claim certain Real players do not want the goalkeeper signed this summer.
Instead, they would rather manager Zinedine Zidane keep faith with Keylor Navas.
The Costa Rica international has been in fine form since arriving from Levante after the 2014 World Cup, helping Los Blancos win the Champions League twice in the past three years.
He nearly moved to Old Trafford as part of the De Gea deal in 2015 but has since firmly established himself as the club's No1.
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Real Madrid players want Keylor Navas to stay in a huge boost for Manchester United
Any arrival of the United star would plunge his own future into doubt and the 30-year-old would likely be reluctant to play second fiddle at the Bernabeu next season.
It is said club captain Sergio Ramos is leading calls from inside the Real dressing room for Navas to stay.
Others players are said to echo this statement feeling that, with Navas between the sticks, their dominance of Spanish and European football can continue.
It means United now have fresh hopes of keeping De Gea, but there was already confidence they could keep him after securing Champions League football for next season.