United are trying to gazump Manchester City's bid to sign Sanchez.
Neville said: "It's pretty obvious he's not going to stay at Arsenal. I think if United were going to buy him, £25m would be an absolute snip. They missed out on buying Ivan Perisic in the summer, and with that missed out on a winger. I think Sanchez provides the quality, the goals and the world-class ability he has got.
"I think it would be absolutely unbelievable signing. If you look back at Man Utd's big signings over the decades, Cantona came out of the hat, Van Persie was a surprise, and they both helped United win titles. I think this could have a similar impact.
"It would be a coup, particularly for United fans, to have a player like Sanchez potentially come to them over City. It would be a strong statement.
"The character that Jose Mourinho wants is that of a typical Man Utd player. Skill isn't always at the top of the list, it's the determination, character, willingness to work hard, and if you think of these traits, Sanchez has them in abundance."
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