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The centre-back moved to Old Trafford in 2010 and has racked up 243 appearances for United.
The Spurs defence was the best in the Premier League last season, only conceding 26 goals - seven less than champions Chelsea - but Pochettino is still seeking to add reinforcements.
They are also make slow advances in their pursuit of Real Madrid striker Alvaro Morata. United also remain linked with ex-player Michael Keane, who looks set to leave Burnley for a bigger challenge. Daley Blind is seen as a left back, who is most likely to have increased playing time next season, as Luke Shaw is expected to leave the club in the summer transfer window.
Ahead of the summer, the Portuguese provided a wishlist to Ed Woodward which included players in England in each position.