Neville believes the Japan international could make similar impact as Javier Hernandez and Ole Gunner Solskjaer.
Kagawa joined United in a £12million deal from Borussia Dortmund earlier this summer.
“As for the transition into the English game, I think it should be easy for [Kagawa]. He’s played at Dortmund, a very professional football club and one of the biggest in Germany. He won’t have any trouble adjusting to the English game,” Neville told the club’s official website.
“I’m really excited about watching him play and seeing how he fits in with the other talented players in this squad. He’s had a fantastic couple of seasons at Dortmund, who have been magnificent in Germany.
“It’s not easy to knock Bayern Munich off their perch. And if you look at the performances, Kagawa has played a big part in that.
“He might be one of these lads that comes to United and sneaks under the radar a little bit. He’s not what you’d class as one of Europe’s stellar names at the moment. But he could be somebody who has the same sort of impact as Chicharito or Ole Gunnar Solskjaer and go on to become a real sensation for United.”
He continued: “The manager’s philosophy has always been to get deals done early and get the new players on tour so they can see what the dressing room is like and settle in.
“You can guarantee that by the end of the tour they’ll feel like they’ve been a Manchester United player for a long time.
“You hear stories about other clubs where new players don’t feel particularly welcome. I can say with confidence that the manager and the players at United would never let that happen. Everybody’s made to feel very welcome straight away.
“Pre-season’s great for integrating new signings into the set-up. For those two or three weeks you’re living in each other’s pockets, you don’t see your friends or family… your team-mates are all you’ve got. It’s a great way to introduce new players to the club.”