The People says the Japanese midfielder has struggled for games since David Moyes took over and has now told team-mates that he needs to leave Old Trafford in the transfer window.
Kagawa, 24, fears he will continue to be frozen out of the United side in the build-up to the World Cup, and does not want to risk a lack of fitness and form as he heads to Brazil.
He arrived in June 2012 in a deal worth around £17million from Borussia Dortmund.
The German club enquired about re-signing him in the summer, and Bundesliga side Wolfsburg have declared that they will be in the hunt to snap him up too if he becomes available.
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