According to the French publication Le 10 Sport, the defender will leave Parc des Princes in the summer transfer window. He has been attracting interest from the Premier League, with the Red Devils believed to be in the driving seat for his signature.
Aurier is wanted by United manager Jose Mourinho, who plans to make the right-back his fourth signing of the summer transfer window. The Mirror reported Paul Pogba and Romelu Lukaku's agent Mino Raiola is working as a mediator between United and Aurier's representative Stephane Courbis.
The Ivory Coast international has reached an agreement in principle with the 20-time English champions. Should he complete a switch to Old Trafford, he is expected to earn around £90,000-a-week ($118,278 per week).
Le 10 Sport claims that Chelsea have now entered the race in signing the former Lens and Toulouse defender this summer. The Premier League winners are looking to challenge United in signing Aurier, despite reports that the player has an agreement in principle with Mourinho's side.
PSG value Aurier around €30m (£27.1m, $35.6m) and the potential suitors should meet their asking price. Any move from either United or Chelsea for the 24-year-old will not take shape until next week as he is set for a court hearing in France.
Aurier assaulted a police officer outside a nightclub in Paris last September. He was handed a two-month prison sentence after being found guilty by the French court. The United Kingdom (UK) Home Office pulled his visa and is currently banned from entering the country.
This saw him miss PSG's Champions League group stage fixture against Arsenal last season. The right-back has lodged an appeal against his conviction in the French courts, which is due to heard next week. Aurier can only commit to either United or Chelsea after the next week's verdict
PSG have already signed Dani Alves on a free transfer this summer and the former Barcelona star is expected to be the first choice right-back for the 2017/18 season. The Ligue 1 outfit already informed Aurier that he is no longer in their plans and will allow him to leave if the interested clubs can match their asking price of €30m.