Club legends such as George Best, Eric Cantona, David Beckham and Cristiano Ronaldo have worn the number in the past.
Following Michael Owen’s departure from the club in June, Valencia asked Sir Alex Ferguson if he could take up the mantle – and Neville feels that the winger can be a worthy bearer of the historic number.
"He’s been a fantastic signing for United and thoroughly deserves that No.7 shirt," the former defender told the club’s official website.
"Having played with him for a year or two, I can tell you he’s a brilliant footballer, especially to play behind as a right-back. He does the right things at the right time, he works back to help out when you don’t have the ball, he delivers good crosses and he can beat a man.”
Valencia arrived at Old Trafford from Wigan for a fee of around £16 million in 2009 and has since gone on to cement himself a place in the first-team before being named the players' and fans' player of the season in 2011-12.
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"He’s a real handful to play against and I was really pleased to see him score a few more goals last season. That’s probably the only area of the game in which you’d like to see an improvement," the England coach and TV pundit argued.
"He has a wonderful shot and he stays calm under pressure. I’d love to see him chip in with 10 or 15 goals this season - he’s more than capable of doing that."
Valencia’s vacated No.25 shirt has been given to new signing Nick Powell, recruited from Crewe Alexandra in the close-season.