The Reds boss is impressed by how quickly his summer signing picks up new techniques in training without the need for translation.
Shinji has vowed to learn English to the best of his ability but, in the meantime, he appears to be having no problems settling in on tour.
"The thing that's impressed me is that every exercise we do on the training ground, he's never needed it to be explained," Sir Alex said of the Japan midfielder.
"After one demonstration he joins in, as if he's known the language forever. We know he doesn't speak the language, but it isn't a problem.
"It just goes to show that a good footballer can pick up exactly what's needed. He's been fantastic in that respect."
Since his arrival from Borussia Dortmund, Kagawa hasn’t taken long to win over his team-mates, either.
"I've been very, very impressed," Rio Ferdinand said. "He's quick, he's sharp, he has great awareness, he plays off both feet.
"I'm excited about playing with him and getting the season started. I think he'll be a great acquisition."