The shirt, famously worn by the likes of Bryan Robson, Eric Cantona, David Beckham and Cristiano Ronaldo to name but a few, was unoccupied following Michael Owen's summer departure.
ManUtd.com announced on Wednesday that Valencia had asked for the shirt and Neville feels he is a fitting addition to the no.7 club.
"He’s been a fantastic signing for United and thoroughly deserves that no.7 shirt," the former skipper told ManUtd.com.
"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.
"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.
"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."