The 28-year-old England international has been linked with a move away from the London club this summer and Manchester City have been tipped as a potential destination.
Neville believes that Manchester United do not have enough quality to win the Premier League title this season but the signing of Kane could prove to be a game-changer for the Old Trafford outfit.
It is no secret that Manchester United need to sign a top-class striker especially with the likes of Anthony Martial and Marcus Rashford failing to score goals consistently.
The Red Devils are currently reliant on Edinson Cavani and Neville believes that the Uruguayan striker will need to be replaced soon.
Kane is apparently looking to join a club where he can win major trophies and Manchester United certainly have a squad capable of challenging for the highest honours.
The Red Devils have already splashed out on the transfers of Jadon Sancho and Raphael Varane this summer and it will be interesting to see if they can cough up the kind of money required to sign Harry Kane.
A fee of around £150 million could be required to sign the England international.
However, he is one of the best strikers on the planet and a player like Kane guarantees goals every season.
Neville said: “They’re still going to have to replace [Edinson] Cavani and Martial next summer. Martial’s not going to do it, Cavani has only got one year left [on his contract].
“They’re going to have to buy a centre forward at some point. Why not get the man now and give Ole that impetus to get to that 90-point [target]. I don’t think they can with just Sancho and Varane.
“Manchester United will lose Martial and Cavani in the next 12 months, they’ll only have Mason Greenwood as a centre forward, [Marcus] Rashford [is best] on the left.
“I think Manchester United will need a centre forward in the next 12 months, the guy is available now if you pay £150m.
“You’ve got Martial, James, Mata and Lingard who I think, to be fair, we could do without them at the club. I personally think Kane coming in [to United] would be a differentiator.”