Aurier's days in the French capital look to be numbered following the arrival of Dani Alves at the Parc de Princes with Belgium international Thomas Meunier set to provide cover for the Brazilian this season.
L'Equipe reported in July that PSG have been listening to offers for the former Toulouse right-back, asking for a fee in the region of €20m to €25m (£18m to £22m).
United were quickly credited with interest in the powerful full-back with Goal suggesting last week the 24-year-old was poised to sign a five-year deal after coming to a verbal agreement with the Old Trafford club to compete with Antonio Valencia down the right flank.
However, latest reports suggest Aurier is entertaining a number of offers, including one from United's Premier League rivals Tottenham with a five-year contract agreement in place with the north London club. L'Equipe also credit Serie A duo Inter Milan and Juventus with keen interest, although the player is said to prefer a move to the Premier League.
However, both United and Tottenham face a major stumbling block in signing the Ivory Coast international this summer as it is currently uncertain whether he would be given permission to enter the UK amid an ongoing legal issue.
Aurier was given a suspended two-year prison sentence for attacking a police officer in 2016, an incident which saw him barred from entering the UK last November when his visa application revoked by the Home Office ahead of a Champions League tie with Arsenal.
Aurier is awaiting the outcome of an appeal but with just 16 days of the transfer window remaining, the clock is ticking.
United could still be in the market for another right-back with a potential problem looming should they lose Valencia to injury. While Matteo Darmian can provide cover, the Ecuadorian's pace and power has become vital for Jose Mourinho's set up at Old Trafford. Having allowed Timothy Fosu-Mensah to join Crystal Palace on a season-long loan, the club have no real option to replicate that should 32-year-old Valencia not be available.
Tottenham meanwhile sold first-choice option Kyle Walker to Manchester City for £50m this summer but still have Kieran Trippier among their ranks. Nineteen-year-old Kyle Walker-Peters was given his senior debut at right-back on Sunday [13 August] in the comfortable win over Newcastle United, picking up the man of the match award after an impressive performance.