The Tottenham forward, who told Spurs at the end of last season that he wanted to leave the club this summer, is a target for United rivals Manchester City, who have been denied an offer of 100 million pounds for Kane.
However, Neville believes his former club United should make a move for the England captain before the transfer window closes on Tuesday, August 31.
The Sky Sports expert compared United’s progress under Solskjaer to Liverpool’s early years under Jurgen Klopp, but said the Anfield club’s major advance in Klopp’s fourth season was fueled by the arrivals of Alisson and Virgil van Dijk.
Neville believes Kane could have a similar impact for United …
« [Manchester United] obviously had those chaotic years after Sir Alex Ferguson with David Moyes, Louis van Gaal and Jose Mourinho. Chaotic in terms of the treatment of managers, chaotic in terms of transfer strategy but also signatures, very reactive.
“They’ve completely changed over the past three seasons. I think what they are looking at is probably the Sir Alex Ferguson era where the club were patient but also they will be watching Liverpool. Jurgen Klopp had time to build a team, to progress slowly from year to year.
“If you look at Ole Gunnar Solskjaer’s first 99 games, which he has now, and Jurgen Klopp’s first 99 games, they’re almost right in terms of performance – 1.89 points per game for Jurgen Klopp and 1, 86 points per game for Ole Gunnar Solskjaer.
“Jurgen Klopp, fourth in points per game, Ole Gunnar Solskjaer third. Jurgen Klopp with a winning percentage of 54%, Ole Gunnar Solskjaer 53%. Again, shoulder to shoulder.
“The exceptional thing, Jurgen Klopp’s ridiculous training performance, comes down to the fact that he did it with a profit of £ 30million, a great recruiting performance from Liverpool and himself, while Manchester United spent £ 314million during Ole’s time.
“The most important thing is what happens next.
“I’m sure the team at Ole’s backroom and the board are looking at him and saying, ‘He’s building something, that’s what Jurgen Klopp was doing at Liverpool during his three first seasons. “
“However, you just have to look at the points Jurgen Klopp earned from season three to season four.
“That was the moment Alisson walked in, Virgil van Dijk walked in, and they went turbo boost and delivered one of the best performances you’ll ever see.
“I know they were beaten by Manchester City that season, but it was a stunning performance from Liverpool – 97 points and 99 points two seasons on the rebound.
“Manchester United with 74 points in the third season, Liverpool with 75. Can Ole Gunnar Solskjaer get the extra 20 points to win the title?
“My intuition is [new United signings Jadon Sancho and Raphael Varane] won’t have the same impact on Manchester United as Alisson and Van Dijk to bring them to the 90-95 points they’ll need to win the league. I think they will be still short.
“Chelsea, you see what they did with Romelu Lukaku. You see Van Dijk has returned for Liverpool. You can see City has come for Jack Grealish and Harry Kane. If they get Kane there will be a huge problem for United.
“I find it hard to understand why Manchester United are not taking that extra step in this transfer window.
“When it comes to Manchester United, they’ve always looked for the best player in the Premier League, the best English or British player in the Premier League, historically.
“Anthony Martial, Daniel James, Jesse Lingard, you talk about potentially offloading a lot of wages there, potentially getting transfer fees.
“Why don’t they go for Harry Kane this week?” Because I think if Harry Kane got into Manchester United you could get up to 90-95 points.
“Without him, they will still have to replace Edinson Cavani and Martial next summer. Martial is not going to do it, Cavani is only one year old.
“They’re going to have to have a center forward at some point, why not ask the man now to give them the momentum to get to those 95 points?” Because I don’t think they can do it just with Sancho and Varane.
“With the manager, I still think you could say he has to prove himself quickly because I still think the Europa League final was bad. It’s going to crash if something goes wrong this season.
“But I think Ole still deserves 12 to 18 months of construction because Manchester United tried Jose Mourinho’s quick kick and it didn’t work. Louis van Gaal, going for a different style of play, it didn’t work. It has failed miserably. .
“So they opted for someone who brought it back to its roots. He must have a chance to do it. Manchester United are going to need a new center-forward in the next 12 months, the guy is available now if you pay £ 150million.
“I personally think the arrival of Kane would be a differentiator. “
Follow the summer transfer window with Sky Sports
You can follow all the latest transfer news and rumors in our dedicated Transfer Center blog at Sky Sports’ digital platforms, as well as to follow all developments on Sky Sports News.