The legendary goalkeeper is looking for a new challenge after ending his 17-year stay with the 'Old Lady' with yet another Serie A title.
There has been interest from a host of sides, including West Ham and former club Parma, but according to the aforementioned source, it is PSG who lead the race.
Initial discussions over a two-year deal in the French capital are believed to have gone well, with further talks planned on Monday and Tuesday.
The 40-year-old has been offered a coaching role at Juve, but he is keen to continue playing.
Buffon's appearance against Hellas Verona at the weekend was his 656th and final for Juve, with more than a tear or two being shed as he bid farewell to the club that became his home.