Speaking after United's 4-2 victory over local rivals Manchester City on Sunday, Neville feels his former employers must do everything in their power to keep the much-improved De Gea, but admits there is a chance the Spain international will join Los Blancos as early as this summer.
De Gea will have 12 months left to run on his contract at the end of the season and United will need to seriously consider cashing in on the 24-year-old if it transpires that he favours a move to the Bernabeu.
Neville urges United to sign a Real Madrid player
But Neville feels United should only do a deal with Real Madrid - the likely destination for De Gea - if they can sign a player in return.
"United need to try and keep him," he told Sky Sports, according to the Mirror. "If they’re not going to keep him, there’s only one club you can think of that is going to come in for him. United have got to take someone off them.
“He has settled down now and is performing fantastically well. He’s been the best player for United all season, and he’s a candidate for player of the season.
“When this club - and any club for that matter - don’t have the goalkeeping position settled, it creates anxiety and nervousness all the way through the team."
Bale or Ronaldo unlikely to join United
Neville may have been referring to either Gareth Bale or Cristiano Ronaldo, who have both been linked with moves to Old Trafford in recent months.
However it's understood Real Madrid have no desire to sell either of their two star attacking players, while Los Blancos are also expected to retain the services of highly-talented centre-back Raphael Varane.
Real Madrid, if they sign De Gea, will look to sell at least one of their current batch of goalkeepers, with long-serving captain Iker Casillas the most likely to depart the Spanish giants this summer.
But Manchester United will have no interest in signing the 33-year-old Casillas, who has declined significantly over the past two seasons, while Keylor Navas might be regarded as a similarly unattractive option in the eyes of Louis van Gaal.
Question marks over Victor Valdes
Should De Gea leave, United possess a ready-made replacement in the form of Victor Valdes, the former Barcelona goalkeeper who penned an 18-month deal with the Red Devils in January.
But it's now a year since Valdes last played a senior professional match, and there are concerns that the 33-year-old is no longer the player he was.
De Gea is in a small group of world-class goalkeepers, alongside Bayern Munich's Manuel Neuer and Chelsea's Thibaut Courtois.
Inevitably, then, any replacement for De Gea will be a downgrade for Manchester United.
Who should Manchester United replace David de Gea with if the Spaniard leaves Old Trafford this summer? Have your say in the comments below!