The People reports that Kagawa is keen to leave as he does not want to risk a lack of fitness and form ahead of the World Cup.
The Japanese midfielder has not been a regular at Old Trafford since David Moyes took over as manager.
The 24-year-old has reportedly told team-mates that he needs to leave United in January.
Kagawa joined United from Bundesliga giants Borussia Dortmund in a £17million deal in June 2012.
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The start of the 2017-18 Premier League season is just around the corner and is shaping up to be one of the most competitive yet.
As always it is the so called “big clubs” that have splashed the most cash in the transfer window so far this summer. Manchester United or City? Arsenal or Tottenham? Who are the winners and losers of the transfer window so far?