The Japan international says he was pleased to be part of both a league-winning side and also Sir Alex Ferguson's last season.
The Japan international moved to Old Trafford last summer but found himself in and out of the side, resulting in a return of six goals in 26 appearances.
Dortmund, meanwhile, reached the Champions League final, where the club was beaten by Bayern Munich, and Kagawa says he would like to return there one day.
"Yes, one day I will [return to Dortmund]. If Dortmund are ok with it," he told ‘Foot x Brain’ on TV Tokyo.
The 24-year-old then spoke about his satisfaction at playing under Sir Alex Ferguson in his final season in charge of United.
"I'm happy we won the league but I'm not satisfied with my performance," he said. "The club has a long history and it was great that I could play in Sir Alex Ferguson's last season.
"At first there were also moments when I felt a bit lost but I tried not to give too much importance on such a feeling."
Kagawa has also revealed his determination to improve ahead of the upcoming season and also next year's World Cup in Brazil.
"All I can do is keep showing what I can," Kagawa continued. "I have no excuse any more after a year in the Premier League. I know I'm at a place where you can't play if you don't achieve results. I'm determined to do it, also because there will be a World Cup.
"It's really an important year for me."