Dealings between PSG and United have been ongoing throughout the summer with the English club also attempting to negotiate an agreement for midfielder Manuel Ugarte.
Sancho starred against PSG in last season's Champions League semi-final at a time when his United career looked over after joining Borussia Dortmund on a temporary loan deal.
Dortmund were hoping to negotiate Sancho's return to the club on a permanent basis but have been priced out a move for the England international - a scenario not likely to affect PSG.
The reigning Ligue 1 champions have already held discussions over a transfer for Sancho who has two years remaining on his contract at Old Trafford with the option of an extra year.
Sancho starred against PSG in last season's Champions League semi-final while representing Borussia Dortmund
The 24-year-old was banished from United's first-team last year when he hit out at manager Erik ten Hag after being criticised over his performances in training following a defeat against Arsenal.
Sancho at the time insisted he was being made a 'scapegoat' and subsequently refused to apologise to Ten Hag who decided there would be no way back for their relationship unless an apology was issued.
The pair have since made up and Sancho has been an influential figure in United's pre-season tour of the United States, with Ten Hag recently claiming he could be deployed as a striker this season.
United are keen to bring in further reinforcements ahead of their Premier League season-opening game against Fulham on August 16, but need to raise funds by selling other players.
Scott McTominay has also been discussed as another potential departure with United already rejecting a £20m offer from Fulham as they attempt to hold out for a higher fee for the Scotland international.
United are continuing to monitor Ugarte's situation in Paris but are exploring other options as PSG hold out for over £50m and have since made initial contact over a deal for Monaco's Youssouf Fofana - who is also a target for AC Milan.
Burnley's Sander Berge and Richard Rios of Palmeiras are also among those appreciated by United.