The Japan midfielder has not figured since the Community Shield win over Wigan last month and missed Saturday's win over Crystal Palace with a mild flu virus.
However, it does appear Kagawa is in contention to face the German side on Tuesday night in what will be David Moyes' first group game in the competition.
Absent from training on Monday morning were Danny Welbeck (knee) and Phil Jones (ankle), while 18-year-old Belgian Adnan Januzaj was not present either, Moyes having opted not to select the 18-year-old in his Champions League squad.
Striker Wayne Rooney was able to train without the distinctive headband he wore on Saturday's game.
In addition, midfielder Darren Fletcher was a welcome sight given his long health problems, although he trained away from the main group.
United are favoured to advance from a group that also includes Shakhtar Donetsk and Spanish dark horses Real Sociedad.