Everton have been strongly linked with a move for the Dutchman in the wake of Yannick Bolasie's injury, suffered ironically against United earlier this month.
Signed from PSV Eindhoven for £25 million in 2015, Depay has struggled to rediscover the form which saw him finish his final season in Holland as the Eredivisie's top scorer.
The 22-year-old has been used on eight occasions by Jose Mourinho and only one of those appearances came as a starter.
Though the presence of fellow Dutchman Ronald Koeman could lean Depay in the direction of Goodison Park, Everton will no doubt be wary of being gazumped by Tottenham for the second time in recent months, after Moussa Sissoko's £30 million switch to White Hart Lane.
Sissoko has spent much of his early Spurs career shoehorned into a wide role, and the arrival of Depay would perhaps allow the Frenchman to concentrate on his natural game in the centre of midfield.
The London Evening Standard reported on Wednesday that Tottenham boss Mauricio Pochettino is also considering a January move for Everton midfielder Ross Barkley.
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