The 27-year-old had extensive tests at the Aspetar sports hospital after being given permission by the Premier League giants to fly to the Qatari capital for talks with PSG officials.
— Aspetar سبيتار (@Aspetar) August 4, 2015
The two clubs have already agreed a fee of £44.3 million (63 million euros; $68.9 million dollars) for Di Maria who will end his one-year stay at Old Trafford.
United snapped up Di Maria for a British record £59.7m from Real Madrid last summer, but the winger’s form slumped dramatically after making an encouraging start to life in north-west England.
After netting three goals and making four assists in his opening six games for the 20-time English champions, Di Maria spent time on the sidelines with injury and fell out of favour with Red Devils boss Louis van Gaal.
He started just one of the final ten games of last season with his final United goal coming in a 2-0 FA Cup third round win over Yeovil Town in January.
Di Maria was also unsettled off the field after an attempted burglary on his home in Cheshire in February.
Since that incident, the Argentine has been living in a city-centre appartment in Manchester — owned by former United player Phil Neville — with his family.
The former Benfica player had said he wanted to stay at United but after failing to report for the second part of the club’s pre-season tour of the United States on July 25, his future at Old Trafford appeared to be over.
Di Maria — who has 65 caps for Argentina — scored four goals in 32 appearances for United.