The Times reports that several Premier League clubs are hoping to sign the 20-year-old on a loan deal in January.
Zaha is considered one of England’s top football talents and joined United from Crystal Palace over the summer.
The youngster featured for United in the Community Shield win over Wigan in August but has not played since.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.