According to SFR Sport via Get French Football (h/t Jack Otway of the Daily Express), the Ivory Coast international is seeking a switch to Old Trafford, but Spurs have offered PSG more money for the full-back.
Paul Pogba has encouraged United to move for the player, but a transfer to Spurs remains more likely before Thursday's transfer deadline at 11 p.m. BST.
Jason Burt of the Telegraph reported Spurs have agreed a £23.1 million price for Aurier's services as they seek a replacement for Kyle Walker. However, the north London club are checking their legal position before executing a transfer due to the player receiving a two-month prison sentence for assaulting a police officer. The issue had denied Aurier entry into the UK last November as he failed to gain a visa.
Per L'Equipe (h/t sportswriter Jonathan Johnson), Aurier is set to hear on Tuesday if he will be granted his wish for a move to England:
Aurier has previously been rated as one of the most dynamic full-backs in Europe, but the arrival of Dani Alves and Neymar have squeezed PSG's options.
United currently play Antonio Valencia at right-back, but the Ecuador international is not a natural defender and struggles to provide consistent service of the highest calibre.
Aurier featured in 22 appearances in Ligue 1 last season, according to Squawka, creating 23 chances with an 89 per cent average passing accuracy.
In other news, Chris Smalling could be shown the door at Old Trafford as manager Jose Mourinho decides on who he wants to retain.
According to the Mirror (h/t Jack Staplehurst of the Daily Star), Leicester City are exploring the possibility of tempting the England international. Mourinho has plenty of cover at centre-back, and the form of Phil Jones has seen him become first choice with Eric Bailly.
Smalling started only 13 Premier League games during Mourinho's first season in charge, per WhoScored.com, and the signing of Victor Lindelof will limit his starts this year.
The defender has been a fine servant for United since signing from Fulham in 2010, winning two Premier League crowns during his spell.
Mourinho has stockpiled a fine selection of central defenders, and Smalling will need to play elsewhere to retain his standing in the England squad.
Leicester have increased balance under manager Craig Shakespeare, and the addition of Smalling would give them the defensive leadership they crave at the King Power Stadium.