The former England full-back believes that Kane is England's genuine world-class player, and that the striker has to have a good tournament if England hope to do well in Russia.
"World class for me is defined by the question: would he get into any other team in the tournament? And I think he would. Other teams would have to find a place for him, he's that good," he explained.
"He's a stable character, strong mentally and capable of withstanding physical knocks. He's a brilliant player, and England have an outstanding, world-class striker."
Kane managed to bag both goals in the Three Lions' opening fixture, but came under some criticism in the match for not holding up the ball to allow his team-mates to get more attacking opportunities.
Neville also believes that it is crucial for Everton 'keeper Jordan Pickford to be on top form in his country's game, despite barely being called upon in the Tunisia victory.
"I've said from the start, Harry Kane and Jordan Pickford have to have good tournaments for England to do well at both ends."
Overall, the former assistant of the national team under Roy Hodgson believes that there is room for improvement, but encouraging signs.
"Areas of caution? I suppose missing chances in the first half. I think England will always be stronger in the first 50-60 minutes of a match, because of the way we play."
England will face their next match against Panama on Sunday, with their final and most challenging group match coming against Belgium.