The Tottenham striker had a phenomenal season in 2014/15, and the former Manchester United defender has said he would be ideal for Louis van Gaal's side.
Neville stressed how impressed he had been with the way the 21-year-old had taken to the top level of football in what was his breakthrough season in the Premier League.
"He was unbelievable last year and I am a big fan of Harry Kane," the 38-year-old told Sky Sports News. "I love the way he goes about his business.
"He works hard and has a great attitude and nothing seems to faze him, he's answered every question that has been thrown his way."
Kane scored hatfulls of goals in the Europa League, the Premier League and for the England Under-21s last year, while in March he scored on his full England debut against Slovenia.
There are few strikers who have enjoyed such a spectacular rise, and Neville thinks the forward, who is preparing for the European Under-21 Championships later this month, can go one level higher by joining one of the biggest sides in the world in United, who themselves are returning to the Champions League.
"The team and the club has always had a backbone of British players," Neville said of his old side. "I think that is still important, that you get British players and the spine of the team has that British feeling."
But the former England defender admitted any attempts at doing business with Spurs may be impossible, with Daniel Levy stating Kane won't be sold, and the striker himself a boyhood White Hart Lane fan.
"He (Kane) would cost a lot of money that's for sure and I'm sure Tottenham don't want to lose him," he warned.
"But I think with losing Falcao, and being in the Champions League, United have (Robin) Van Persie, (Wayne) Rooney and (James) Wilson so they probably do need one more striker and the type of signing that Man Utd will make this summer will be a signing that will be a quality player from European football whether that is England or abroad.
"Kane fits that bill and if they can get Harry Kane here that would be a fantastic signing."