The Daily Express says Tottenham were interested in Martial over the summer, and could reignite that interest in January.
It's suggested Spurs could look to propose a swap deal with their own unhappy Frenchman - defensive midfielder Tanguy Ndombele.
They say United would be interested in Ndombele with Paul Pogba's future uncertain and defensive midfield issues of their own.
Martial has been criticised after his performance in last night's Carabao Cup defeat to West Ham.
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