Having announced that he would be leaving Juventus, the 40-year-old has been offered a two-year deal by the Ligue 1 champions that would see his wages doubled to €8 million per year (£7m/$9.4m).
The Italy international has also been given the chance to live in an apartment overlooking the Eiffel Tower, with PSG hopeful that they can tempt him to prolong his career in the French capital.
His agent Silvano Martina and lawyer Luca Miranda arrived in Paris on Tuesday, with the player himself still in Italy having played in Andrea Pirlo's testimonial on Monday evening.
It is thought Buffon would initially act as an understudy for Alphonse Areola at Parc des Princes, with the PSG hierarchy hopeful that he will be able to mentor the 25-year-old Frenchman.
Buffon has emerged as a target for PSG given their fear that any more lavish spending following the arrivals of Neymar and Kylian Mbappe last summer could see them punished under Financial Fair Play (FFP).
However, with Neymar now desperate to join Real Madrid it could spark a change in policy from president Nasser Al-Khelaifi.