De Gea, 26, has long been linked with a move to the Bernabeu.
He was on the verge of joining the European giants in 2015 only for paperwork problems to scupper the deal at the last minute.
Keylor Navas has since emerged as the Spanish club’s first-choice goalkeeper.
He made 41 appearances in all competitions last season as Real claimed a first league title in five years and secured back-to-back Champions League triumphs.
Diario Gol claim manager Zinedine Zidane is willing to keep faith in the 30-year-old Costa Rica international for the time being.
And club president Florentino Perez had apparently lined up AC Milan starlet Gianluigi Donnarumma as his long-term replacement in between the sticks.
But the youngster now looks set to pen a new contract at the San Siro.
According to Diario Gol, that has prompted Perez to reignite his interest in De Gea.
He is said to have contacted Jorge Mendes, De Gea’s agent, to resume negotiations over a deal for the Spain international.
And if Real fail to land him once again, Chelsea’s Thibaut Courtois reportedly remains a back-up option for the Bernabeu outfit.
