Neville, who hung up his boots in 2011, played alongside the striker for seven years at United and now works with him as part of the former defender’s coaching role with the England national team.
Chelsea have so far had two bids rejected for Rooney as speculation over his future at the Red Devils intensifies.
The 27-year-old has scored 197 goals in 402 appearances for United since joining from Everton and Neville is adamant that the Premier League champions must keep hold of the England forward.
"Manchester United, at this moment in time, would be mad to sell him," Neville said in an interview in The Daily Mail.
"Along with Robin van Persie, he has been the most successful player in terms of goals and assists in the last five years of the Premier League.
"Even last year, which you could argue was a year he was below his best, but he was playing in midfield, playing right side, left side, he still had 22 goals and assists.
"He is a massive contributor to games and you can’t replace personalities. There are very few personalities in football now, big personalities, fighters, he is one of them.
"You can't just buy them, you might argue you could replace them in respect of the numbers he creates but in terms of personality, what he brings, very difficult to replace him. I could argue in the last eight years, he has been the most important player in the Premier League.
"Why would I be over the top by stating that? He is one of the most successful players in the last eight years, won the most championships in that period, been an ever present, played in every single game nearly every season.
"Scoring 20-plus goals in most of them, assisting, fighting for every single ball in every single game. The evidence is there – they don’t grow on trees, Wayne Rooneys."
Rooney is currently away on international duty with England and could feature in Wednesday's friendly against Scotland, despite a shoulder injury forcing him to miss Sunday's Community Shield win over Wigan Athletic.