Kagawa joined up with his United team-mates for the first time since May on Monday as United arrived in Japan on the third stop of their tour.
And although Kagawa is not expected to feature in Tuesday night's game against Yokohama F.Marinos, Moyes says he has had positive reports from predecessor Sir Alex Ferguson about the 24-year-old.
"I know a little about him as a player," said Moyes.
"Sir Alex spoke in glowing terms about Shinji and how good a player he is. I've just met him today, so we're getting to know each other. I'm trying to learn Japanese and he's trying to understand my Scottish.
"It was his first season in the Premier League last year. He's a young player so we hope his development continues. I look forward to working with him and hopefully he has a really good season coming up."