The Brazil international returned to Barcelona after spending the 2019-20 season on loan at Celta Vigo, where he amassed four goals from 29 La Liga appearances.
However Rafinha, whose contract at Camp Nou was due to expire next summer, has not made an appearance for La Blaugrana this season and looks set to secure a move to the Ligue 1 champions.
According to Marca, the midfielder is heading to the Parc des Princes on a free transfer which includes €3m (£2.7m) in bonuses, and Rafinha will be announced as a PSG player assuming he passes his medical.
The report claims that Barca had initially hoped to garner €16m (£14.5m) for the 27-year-old - which ultimately failed to come to fruition - and La Blaugrana will also receive 35% of any future sale of Rafinha.
Rafinha - an academy graduate of Barcelona - has scored 12 goals from 90 appearances during his time at Camp Nou, winning three La Liga crowns in that time.