With rumours suggesting they could offer £50m for the versatile 23-year-old, who can also play in defence, while doubling his wages to £140,000-a-week which is way beyond any figure Tottenham could match, teaming up with Mourinho for the Europa League winners could be an opportunity too hard to turn down for both Dier and Spurs financially.
Still, Spurs' current stance is that Dier isn't for sale, with the Lilywhites possibly hoping to cash in on United's desperation later on in the window.
Dier is understood to be interested on a move to United - the team he supported as a boy - where he would be deployed in his favoured role, and would expect to earn significantly more money given Spurs' controlled wage structure. Lukaku joined United from Everton on Monday for a fee that could rise to £90m.
If Levy were to block Dier's transfer, what would he do about his salary?
Dier has not always been able to play in his preferred position in midfield following the arrival of Victor Wanyama at White Hart Lane and a move to Old Trafford could suit him.
Levy may face a dilemma when United's offer is broken down.
The 21-year-old Brazilian has been taken on the club's pre-season tour of the United States, having spent last season on a season-long loan with La Liga side Granada.
Jose Mourinho certainly seems like a man who knows his football history.
Tottenham will agree to sell Kyle Walker, though Manchester City have yet to meet their £50million asking price, but will not entertain any enquiries for Dier.
Perhaps Mourinho, in his race to finish the post-historical chapter of the book where Manchester United waltzes to the Premier League title in 2017-18, has forgotten a key detail from the past. Pochettino would be less willing to cash in on selling Dier.