This is according to Spanish broadsheet El Confidential, who understand that Real Madrid will pay €40 million (£28.6 million) to United for the Spain international.
De Gea, who will reportedly sign a six-year deal with Los Blancos worth €5 million-a-year, is now waiting for the green light to complete his big-money move to the Bernabeu.
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De Gea has been training with Manchester United this week after arriving back in England, from Madrid, at 1:30am on Monday morning.
He was spotted hiding from photographers in the foot well of a car earlier this week, although he was snapped a day later out shopping alongside compatriots Juan Mata and Ander Herrera.
United no closer to Sergio Ramos deal
It now seems certain that De Gea’s four-year spell with Manchester United is at an end. The 24-year-old had hoped the deal would be finalised before Monday - in order to avoid a potentially awkward return for pre-season training - but the timing of this latest update suggests the transfer will go through before United fly out to the United States next week.
Quite how this might impact Manchester United’s potential deal for Real Madrid’s unsettled defender Sergio Ramos is unclear, although the fact Los Blancos have agreed to pay €40 million indicates the Red Devils are no closer to striking an agreement for the Spanish centre-back.
United have been resigned to losing De Gea since the end of last season, when it became clear the club’s current Player of the Year had no interest in signing a contract extension.
Will Van Gaal sign a new goalkeeper?
Louis van Gaal feared this would happen midway through last season and reacted by securing the services of former Barcelona goalkeeper Victor Valdes on a free transfer.
Valdes made his United debut at the end of last season and showed enough to suggest he will be perfectly capable of taking De Gea’s place if Manchester United fail to sign a permanent replacement.
The Red Devils have been linked with a move for Tottenham’s Hugo Lloris - although the France international is likely to be too expensive - while Galatasaray keeper Fernando Muslera is another option for the Premier League giants.
De Gea wanted assurances from Real Madrid that he will be the number one goalkeeper at the Bernabeu, ahead of Iker Casillas, who has been strongly linked with a move to FC Porto in recent days.
Real Madrid have granted De Gea his wish and will now bring the former Atletico Madrid starlet back to his home city following a four-year absence.
Manchester United fans have reacted on social media to the news - and here are some of the best tweets.
Manchester United fans: are you relieved the David de Gea saga appears to be nearing an end? Is Victor Valdes good enough to replace him? Have your say by leaving a comment in the box below!