England international Dier's name was on the shortlist Mourinho handed to executive vice-chairman Ed Woodward earlier this year after he watched him impress after Mauricio Pochettino shifted him from defence to midfield during Spurs' 2015/16 campaign.
But Tottenham remain resolute in their stance that the 23-year-old, valued at upwards of £50million, won't be sold this summer.
Chelsea's Nemanja Matic remains the most likely arrival despite the difficulties that Romelu Lukaku's impending transfer from Everton presents with Monaco's Fabinho another option.
Matic's arrival won't preclude United's interest in the Brazilian, however, with Mourinho seeing him as a player who can do more than just play in holding midfield.
Fabinho has been used at right-back by the Ligue 1 champions and Mourinho wants to improve his options in that role too. Last season, Mourinho primarily deployed Antonio Valencia, a specialist winger, there instead.
Should Matic follow Lukaku into Old Trafford he will arrive for a fee of roughly £35m. Matic will leave as soon as his replacement, Tiemoue Bakayoko, joins Chelsea from Monaco with that deal understood to be edging towards a conclusion.
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