Sky sources reported on Friday that United are keen on signing the Tottenham striker, who scored 21 goals on his way to being voted the PFA Young Player of the Year, but Spurs chairman Daniel Levy is keen to keep his star player at White Hart Lane.
Van Gaal has already signed PSV forward Memphis Depay on a four-year contract but he is widely expected to add to his squad during a busy summer in the transfer market.
Neville told Sky Sports News HQ: “He was unbelievable last year and I am a big fan of Harry Kane, 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.
“The team and the club has always had a backbone of British players and I think that is still important, that you get British players and the spine of the team has that British feeling.
“That has been the key success to this club for many years and I hope that would continue.
“He (Kane) would cost a lot of money that’s for sure and I’m sure Tottenham don’t want to lose him.
“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.”