As reported by RAC1 and confirmed to goal.com by sources close to the talks, Abidal, along with board member Javier Bordas, and Andre Cury, a specialist in the Brazilian market, flew to Paris to begin negotiations.
Barca was planning to initiate talks with the Ligue 1 champion and will make an opening offer in the region of €100 million (£93 million/$104 million), 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, is determined to receive as much money as possible for a player it signed for €222 million (£200 million/$249 million) back in 2017, while it also wants right-back Nelson Semedo included in any potential deal.
Sources told goal.com that the French side would consider an offer that includes both Coutinho, Semedo and a cash payment of around €50 million (£47 million/$57 million).
PSG would, however, prefer to sell the Brazilian to Real Madrid, which is planning a €100-million-plus offer of its 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 its supporters appearing to be at an all-time low.
The forward, who didn't feature for the club over preseason, was absent from the Trophee des Champions win over Rennes, while he was also missing from the Ligue 1 opening-weekend victory over Nimes.
Indeed, PSG supporters made their feelings clear as they sang songs and held up banners in protest against the Brazilian's presence in Paris.
There were banners calling for the 27-year-old to "Get out" of the club.
The Ligue 1 side's sporting director Leonardo confirmed on August 10 that there had been talks over Neymar's exit and that they were "more advanced" than previously but that no deal had been agreed.
It remains to be seen if a transfer can be finalized 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.