As reported by RAC1 and confirmed to Goal by sources close to the talks, Abidal, along with board member Javier Bordas, and Andre Cury, a specialist in the Brazilian market, have flown to Paris to begin negotiations.
Barca, as confirmed by Goal, were planning to initiate talks with the Ligue 1 champions and will make an opening offer in the region of €100 million (£93m/$104m), plus Philippe Coutinho.
The Catalans need to offload the Brazilian from their wage bill and had been actively offering him to the Premier League prior to the transfer window closing in England.
PSG, meanwhile, are determined to receive as much money as possible for a player they signed for €222m (£200m/$249m) back in 2017, while they also want right-back Nelson Semedo included in any potential deal.
Sources have told Goal that they would consider an offer that includes both Coutinho, Semedo and a cash payment of around €50m (£47m/$57m).
They would, however, prefer to sell the Brazilian to Real Madrid, who are planning a €100m+ offer of their own, with the relationship between the Parisians and Barca strained after Neymar's initial decision to leave Spain.
Speculation has been rife that the former Santos star has been searching for a way out of Paris, with his relationship with the club and their supporters appearing to be at an all-time low.
"Son of a bitch" was heard being chanted by some of the home fans in the stands at Parc des Princes, while there were also banners calling for the 27-year-old to "Get out" of the club.
It remains to be seen if a transfer can be finalised before the transfer window closes in Spain on September 2 but it's certain to be an intriguing battle as Barca and Madrid go head-to-head.