Kagawa has played just seven minutes in the Community Shield for United so far this season, having not made a single Premier League appearance.
The Sweeper reported earlier in September that the 24-year-old would seek talks with United about his lack of playing time, though it is understood that manager David Moyes has been treating him carefully after appearing at the Confederations Cup in Brazil earlier this summer.
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|6/4||Shinji Kagawa is 6/4 with PaddyPower to score anytime in Man Utd v Crystal Palace
"My position at the club and the national team is different but I'll be able to go back to England in good form and hopefully maintain it at my club. If that happens and I get a chance, I have to work hard to impress on the pitch."
Borussia Dortmund manager Jurgen Klopp has been keeping tabs on his former charge since his move to the Premier League last summer and stated that he would be interested in re-signing the 24-year-old, though the player's agent has dismissed talk of a move.
Dortmund fans have also started a '#FreeShinji' campaign on Twitter, urging their club to bring the attacker back to Signal Iduna Park.
Kagawa was kept on the bench for United's opening league fixture against Swansea City, having travelled back from a Japan friendly earlier that week.
He was not involved in the defeat at Anfield at the beginning of September, with Moyes claiming that he chose Nani instead as the Portuguese stepped up his comeback from injury.