United boss Louis van Gaal appeared to all but confirm that De Gea is set for a transfer to the Bernabeu this summer after Sunday’s 1-1 draw with Arsenal at Old Trafford.
Bale’s future at Real Madrid continues to be a source of speculation following a season of inconsistent performances for the Spanish side.
And former United defender Neville believes that the Red Devils should move to include Bale as part of any deal that would see De Gea leave Old Trafford.
“Real Madrid are particularly aggressive,” said Neville, speaking to Sky Sports after Sunday’s game at Old Trafford.
“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.”
Neville added: “With his [De Gea’s] 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.”
Manchester United, who have secured a top-four finish during Van Gaal’s first season in charge at the club, travel to Hull City in their final Premier League game next weekend.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news