Defeat at Brentford on Saturday has heaped further pressure on United manager Ruben Amorim.
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According to the Mirror, Pochettino is on a shortlist of managers who United are monitoring. Pochettino's contract runs to the end of next year's World Cup.
Former England coach Gareth Southgate is also be considered. As are Crystal Palaces Oliver Glasgow, Fulham's Marco Silva and Andoni Iraola from Bournemouth.
United currently sit 14th on the Premier League table.