Negotiations began on Thursday when Jorge Mendes, the player's agent, arrived at United's Carrington training ground, per the MailOnline's Simon Jones.
However, Sky Sports' Guillem Balague believes Madrid and United have agreed an £80 million "escape" plan, similar to that of Cristiano Ronaldo's before he moved to the Bernabeu.
De Gea has yet to feature for the Red Devils in 2015-16 and appeared to be on his way back to Madrid on the final day of the Spanish transfer window, only to see a proposed move fall through because vital documents didn't get to the proper authorities in time.
A contract extension is fantastic news for United, as the club can now regain leverage in transfer talks with Real. Without it, De Gea was free to sign a pre-contract with any club he desired in January.
While the new deal doesn't rule out a transfer, it greatly increases the chances of De Gea's future playing out at Old Trafford. It also means the stopper will likely return to the starting XI, giving him the consistent playing time he needs in order to make sure he'll be Spain's No. 1 at the upcoming Euro 2016 tournament.