The winger, a British record £59.7m signing last summer, is expected in Doha on Sunday to meet PSG officials.
The fee for the 27-year-old Argentina international is believed to be about £44.5m. Di Maria did not join United's pre-season tour of the United States after appearing at the Copa America in Chile.
The former Real Madrid player moved to Old Trafford last August after helping the Spanish giants to a 10th European Cup in 2014.
But after a promising start, including a goal and an assist in three of his first four appearances, his form fell away midway through the season. He started only one match after a defeat by Arsenal in the FA Cup quarter-final on 9 March.