Kagawa joined United last summer from Borussia Dortmund and says he felt an instant connection with and respect for the 71-year-old manager upon arriving at Old Trafford.
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"He has a magnetic power," Kagawa told United's official website. "I felt it the first time I met him, from the way he conducts himself and also from working with him on the pitch.
"He communicates well with his players and respects them. As the season went on, I got to communicate with him more, both on football and other subjects. That was important.
"He is a friendly person and his spirit is much younger than his age. I think that's because of his achievements over the years, and also his personality.
"I wish I could have played much longer under him. What he has achieved for the club is tremendous - he is in a class of his own."