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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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.