Di Maria joined United from Real Madrid for a fee of 59.7 million pounds ($92.59 million) but, after an impressive start to his Reds career, struggled to display the form that made him one of the most feared attackers in Europe.
Di Maria scored or assisted in three of his first four United games but netted his final league goal in October and only started one match following their FA Cup quarter-final defeat against Arsenal in March.
The 27-year-old did not join the club's pre-season tour of the United States following the Copa America and has been widely linked with a move to the big-spending French side.
British media reported the French side were preparing a transfer fee in the region of 44.5 million pounds ($69.52 million).
Manchester United were unavailable for comment.
On Friday PSG coach Laurent Blanc did little to dismiss speculation that the club were interested in the Argentine.
"As Manchester United and Paris St-Germain are both very big clubs negotiations can be difficult," the former United defender told reporters. "But We feel like we are close to the end."
($1 = 0.6447 pounds)
(Reporting By Tom Hayward, editing by Pritha Sarkar)
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