The 23-year old Japan international ahs not played for the Premier League leaders since sustaining the problem in the 3-2 Champions League win over Sporting Braga in late October but could be back in action soon.
Kagawa was set to be sidelined until later in December but Sir Alex Ferguson has hinted at a comeback in the coming few matches.
"Shinji Kagawa's injury has been longer than we thought. He's much better now and I don't think he's far away now," Ferguson told reporters.
Kagawa could even make the bench for Wednesday night's final Champions League group fixture against CFR Cluj.