England international Rooney is reportedly wanted by Arsenal, Chelsea, Barcelona and Paris Saint Germain after requesting a transfer at the end of last season.
But Three Lions coach Neville, who was a team-mate of the striker at United, thinks the 27-year-old would be making a mistake if he leaves Old Trafford.
Neville said in an interview with Talksport: "I played with Wayne for many years. He's a fantastic footballer.
"Personally, with my allegiances, I'd never recommend anyone leave United, because I believe it is a great stage to play football and you can achieve what you want there."
Neville added: "I've seen David Beckham and other big players leave United and it really is something that comes down to the individual and the club.
"I've seen Ryan Giggs, when he was 27, linked to Inter Milan, Juventus and AC Milan and stay."
Meanwhile, Neville is also backing a change in English football's mentality after the woeful performances of the Under 21s and U20s at international tournaments this summer.
He said: "People have had enough.
"There's a sense now that it's not acceptable to get knocked out of competitions earlier than they should do and for the youth teams not to perform as well as they should do. They've had enough and they want action.
"Growing up in the '70s and '80s, the type of players and football that was played promoted the next generation to play a certain way.
"My hero was Bryan Robson. At Liverpool there was Graeme Souness and at Everton they had Peter Reid. That was the way it was when we were brought up.
"It was all about passion, hard work, getting stuck in, knocking the ball over the top to chase and getting it in the box. We were brought up for 20 years with that mantra.
"We're now starting to see a more technical player and that is what everyone wants to see.
"What we've now seen in the last 15-20 years is a different type of football in the Premier League, people like Dennis Bergkamp, Gianfranco Zola, Thierry Henry, Eric Cantona and Cristiano Ronaldo.
"Parents are now informing their kids about a different message, 'Take the ball, hold on to the ball, stay on the ball and manipulate the ball'."