The Argentine is a free agent after leaving Chelsea by mutual consent on Tuesday.
Pochettino had guided Chelsea to a sixth place and Europa League qualification, but a difference in opinion on several issues saw him and Chelsea's owners agree to part ways.
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The Times says Pochettino is open to speaking to United about replacing Erik ten Hag.
United manager Ten Hag is under pressure at Old Trafford with doubts about whether he has the support of new co-owner Sir Jim Ratcliffe. United end their season on Saturday when they face Manchester City in the FA Cup final.