And that's just as well, as Borussia Dortmund continue to stand firm over their £100m man.
United have been the front-runners for Sancho all summer but missed the August 10 transfer deadline set by Dortmund, meaning it looks like the 20-year-old will be staying put in Germany.
The youngster is said to want a move to Old Trafford, while Red Devils fans are desperate to see the England international arrive.
But Neville isn't worrying about his former side landing Sancho this summer, insisting Ole Gunnar Solskjaer doesn't need to secure a deal.
"The fans I speak to aren't saying we desperately want Sancho," he told Sky Sports.
"They are saying we want the right calibre of signing brought into the club. It could be anybody that fits that bill.
"Yes, Sancho may fit that bill, but I'm not sat here as a United fan thinking I desperately want him. It could be any number of players that become available that would improve United.
"If Harry Kane became available, and Tottenham fans will be saying why are you trying to get him out of Spurs again, but if he became available, he'd obviously improve United's squad. So it doesn't have to be a certain player.
"The emergence of Mason Greenwood takes a bit of pressure off the situation but still, Manchester United need to add to the front three of Greenwood, Marcus Rashford and Anthony Martial.
"They need to challenge those three players and support those three players. They need to have depth behind those three players, and they will drive the standards.
"We saw that with Greenwood, Martial and Rashford towards the end of the season.
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"They were driving each other to score more goals, assist each other, they were playing better together so other players coming in of that kind of quality are going to improve them."
United are looking for a right-sided attacker this summer.
Aside from Sancho, the Red Devils have looked at the likes of Kingsley Coman, Ousmane Dembele and Douglas Costa.