The Spaniard’s present deal expires in 2016 and United had previously indicated they had abandoned hope of the 24-year-old signing an extension.
But following the collapse of a proposed move to Real Madrid on transfer deadline day, negotiations have begun, with De Gea’s agent Jorge Mendes attending the club’s training complex on Thursday.
De Gea is yet to play this season.
Manager Louis van Gaal refused to pick the former Atletico Madrid man until the end of the transfer window, such was the uncertainty surrounding his future, reports the BBC.
De Gea, United’s Player of the Season for the past two years, was upset at Van Gaal’s claim he did not want to play in the opening games of the season, although club sources have since indicated any damage to the pair’s relationship will be easily repaired.
It is still not known whether De Gea will start Saturday’s Premier League game against Liverpool on Saturday (17:30 BST).
Meanwhile, Manchester United manager Louis van Gaal has admitted that the fee paid for teenage French striker Anthony Martial was “a ridiculous amount of money”.
The 19-year-old, who only won his first cap for France after the deal went through, cost a staggering reported fee of £36 million from Monaco just before the transfer window closed last week.
It is believed the fee could rise to £58 million, and Van Gaal, speaking at an event in Manchester for executive United season-ticket holders, said: “It was a ridiculous amount of money, but it’s the crazy world we are in.”
The Dutchman added that the fee reflected a trend of United being routinely quoted “£10 million more” for players.
In addition, he said that Martial had been signed for the club’s “next manager”, and suggested that would be his current assistant Ryan Giggs.
Van Gaal was quoted by The Times as saying: “I have not bought Martial for me – I have bought him for the next manager of Manchester United.”
He added of Giggs, who was alongside him at the event: “I feel I am introducing the next manager of Manchester United.”
