Press Association Sport understands Di Maria is due to hold talks with PSG officials in Doha on Sunday and is expected to undergo a medical with the French champions.
If all goes to plan, he could sign for PSG as early as Monday.
United gave Di Maria permission to speak to PSG after agreeing a 63million euro (£44.3million) fee with the big-spending French club.
United 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 season.
The former Real Madrid winger was left unsettled after an attempted burglary on his Cheshire home in February.
Since then, the 27-year-old and his family have been living in a city-centre apartment in Manchester owned by former United defender Phil Neville.
Di Maria said as recently as June that he wanted to stay at United, but it became apparent that he had his heart set on a move to the French capital in the last couple of weeks.
The Argentinian was due to report for duty during the second leg of United's pre-season tour of the United States on July 25, but failed to show.
After United's 2-0 defeat to PSG in Chicago on Thursday, Laurent Blanc said both clubs were "close" to striking a deal for the former Benfica player.
''Manchester United and PSG are two big clubs and negotiations can be difficult but we are close to the end,'' the PSG coach said.
United manager Louis van Gaal claimed at the time that he had no idea where his star midfielder was.
''I don't know where he is,'' the United boss said.
''You can ask that every week but I don't answer that question.''
Van Gaal is expected to move quickly to sign a replacement for Di Maria
The Dutchman is interested in Barcelona forward Pedro, who was frustrated by his lack of game time at the Nou Camp last season.
Source : PA
Source: PA