After securing their first summer signing in Victor Lindelof earlier this week, it appears as though Jose Mourinho is in a rush to get his business done early if possible.
Smalling managed just 15 Premier League games this past season for the Red Devils and will likely be keen to move on from the club in order to try and win a place in the England squad for the 2018 World Cup.
Both defenders showed a great deal of potential when arriving at the club, yet have seen a loss of form and huge injury issues plague them since then.
Mourinho needs to find a long-term replacement for Michael Carrick - who turns 36 next month - and the Telegraph claim that Dier is the man the Portuguese coach wants on board before the start of the new season.
Dier is said to be his preferred choice with the England worldwide capable of playing in midfield and at centre-back.
Tottenham chairman Daniel Levy's ₤ 50 million appraisal of Dier is greater than United anticipated to pay for the 23-year-old that has actually created substantially under Mauricio Pochettino.
Dier joined Spurs from Sporting Lisbon in 2014 as a raw versatile centre-back but he's developed in to a top Premier League player over the past three years.
Baggies boss Tony Pulis has a put a new central defender high on his wanted list and has already targeted a move for John Terry following his release from Chelsea, however Smalling is also said to be on his wanted list.