The Japan international, who has just been crowned the Asian Football Confederation (AFC) International Player-of-the-Year, was originally set for four weeks out of action but has not recovered as quickly as anticipated.
When quizzed about Kagawa's return by reporters, Sir Alex said: "He's a few weeks away."
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Sir Alex Ferguson's men then travel to rivals City on December 9 and face Sunderland and Swansea before Christmas, with Newcastle the visitors to Old Trafford on Boxing Day.