Press Association Sport understands talks took place between Di Maria and officials from the Ligue 1 champions in Doha on Sunday as the 27-year-old looks to bring to an end a largely disappointing stint at Old Trafford.
United gave Di Maria permission to speak to PSG after agreeing a fee of 63million euros (£44.3million) with the big-spending French club.
The Red Devils signed Di Maria from Real Madrid for £59.7million last summer, but, after an encouraging start, his form dipped drastically and he only started one of the final 10 games of last term.
The winger, who won the Champions League and the Primera Division title during his time in the Spanish capital, was left unsettled after an attempted burglary on his Cheshire home in February
Since then, the player and his family have been living in a city-centre apartment in Manchester.
His future took another turn when United manager Louis van Gaal revealed he did not know of Di Maria's whereabouts when he failed to join up with the squad on their pre-season tour of the United States.
''I don't know where he is,'' the Dutchman said
''You can ask that every week, but I don't answer that question.''
PSG beat United 2-0 before Van Gaal's side returned home to prepare for their Barclays Premier League opener against Tottenham on Saturday.
Former United defender Laurent Blanc is in charge at the Parc de Princes and said he believed PSG were closing in on a deal.
''Manchester United and PSG are two big clubs and negotiations can be difficult but we are close to the end,'' he said after their win over United.
Even before the expected acquisition of Di Maria, PSG continued their dominance of French football by beating Lyon 2-0 in Saturday's Trophee des Champions.
Serge Aurier opened the scoring before Edinson Cavani, a player linked with a move to Old Trafford, added the second.
It is anticipated that Van Gaal will move quickly to sign a replacement for Di Maria
He has hinted at his interested in Barcelona forward Pedro, who was frustrated by his lack of game time at the Nou Camp last term.
Source : PA
Source: PA