The ex-United captain also feels that if Man United are going to have to sell De Gea to Madrid then they should be looking to bring Gareth Bale to Old Trafford.
Born and raised in Madrid, De Gea has constantly been linked with a move back to the Spanish capital.
With only one year left on his current deal, De Gea has up until this point refused to sign a new contract and speaking after the game, Neville said he felt the Spanish goalkeeper’s move to Madrid is going to happen.
“Real Madrid are particularly aggressive,” Neville told Sky Sports’ Podcast.
“They have been previously and once a player only has a year left on his contract Manchester United have a decision to make if Real do come for him, as it looks like they will.
“Manchester City, Chelsea, Arsenal and Liverpool will all want Gareth Bale. So if you are going to give Real a player I think it would make sense to try and get Bale and steal him in return for De Gea.”
With only one year left on his contract, the fact De Gea hasn’t signed a new deal indicates he is considering a move to Spain this summer and it’s something which Neville feels now has an inevitability to it.
He added: “You saw the fans, they were signing his name. You can hear them singing it now as the players do the lap of honour.
“They are singing his name in appreciation of the season he’s had. He’s been Manchester United’s player of the season and they’ll be saying, please stay.
“With his form this season I was always hopeful he’d stay but with the wave of noise in the press it just looked to have an inevitability about it.”