Spurs boss Mauricio Pochettino views Dier, who is valued at around £50m ($64m), as a key member of his squad and has no intention of letting him leave, according to the Mail on Sunday.
United are understood to have sounded out Tottenham over a potential deal for Dier earlier this year, but their approach was rejected. No further talks are believed to have taken place since the end of the season.
However, reports over the past week have suggested that the Red Devils have renewed their interest in the England international after their pursuit of Chelsea midfielder Nemanja Matic suffered a damaging blow.
United struck a £75m deal with Everton for Romelu Lukaku last week – a player that Chelsea boss Antonio Conte was also keen on signing.
Stung by losing the transfer battle for Lukaku, the Blues are reported to have pulled the plug on selling Matic to a direct rival.
Dier has four years left on his Spurs contract but is understood to be keen on moving to Old Trafford, where he would command significantly higher wages and a potential starting berth in United's midfield.
The England international's preference is to play in central midfield, but he was mostly deployed as part of back three alongside Toby Alderweireld and Jan Vertonghen by Pochettino last season.
Dier's sale could also provide Spurs with a much-needed windfall, with the building cost of their new stadium predicted to soar past £800m – double the initial estimate.
Meanwhile, Tottenham chairman Daniel Levy remains open to selling right-back Kyle Walker to Manchester City, provided his £50m asking price is met.
Walker is reported to have clashed with Pochettino over fitness and training and was unhappy at being left out of the team for key matches such as the FA Cup semi-final against Chelsea and the north London derby against Arsenal.
Spurs already have a ready-made replacement for Walker in Kieran Trippier, while the north London club are also reported to be monitoring Porto right-back Ricardo Pereira.