The La Liga giants have long pursued a move for Spain’s first-choice shot-stopper.
Having come extremely close in 2015, Madrid explored the prospect again earlier this summer.
But Jose Mourinho has claimed De Gea is going nowhere and Zinedine Zidane is keen to continue with Keylor Navas.
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The Costa Rica international has had his critics at the Bernabeu but helped win the Champions League last term.
However, Spanish outlet Diario Gol claim Madrid president Florentino Perez will not be denied of De Gea next year.
It is said the club chief has told current No.1 Navas he will stay this season.
But a deadline has been set for the 30-year-old to find a new club by June 30, 2018.
De Gea was not willing to join Madrid this summer if he had competition at the club.
Navas, whose performances left a lot to be desired for in pre-season, refused to go and Zidane insisted he stay, leaving Perez frustrated.
Diario Gol add Perez is not willing to let another summer transfer market pass without getting De Gea.
As a result, Mourinho may have to look for a new keeper after his second season in charge at Manchester United.
Leicester’s Kasper Schmeichel, Atletico Madrid’s Jan Oblak and AC Milan’s Gianluigi Donnarumma were on his radar before.
Reports earlier in the summer suggested De Gea told Mourinho he would stay but wants to play for Madrid at some stage in his career.
