The Spanish club have opened talks with the forward’s current club as they look to close a deal before the transfer deadline.
Club chiefs from both sides were locked in talks on Tuesday in a bid to finalise a transfer involving the Brazilian.
The players position at the club is already in a precarious position, following fan protests against him, and one last push should be enough to seal the switch.
Barcelona are hopeful of tying up a deal for their former superstar, who cost PSG a world-record £198 million just two years ago.
The French champions are said to be keen to structure a deal which would see them recoup that amount and make a profit.
Philippe Coutinho is likely to be part of a player-plus-cash transfer as he finds himself surplus to requirements at the Nou Camp.
PSG are open to taking Coutinho in the negotiations, which was agreed in Tuesday’s meeting.
Barca director of football Eric Abidal and board member Javier Bordas flew to Paris for showdown talks with PSG sporting director Leonardo and intermediary Andre Cury.
The Catalan club reportedly offered £110m plus Coutinho in exchange for Neymar, but that fell short of PSG’s valuation.
They deem Coutinho to be worth around £55-75m following his difficult period in Spain, which is far less than Barca – who value him at £120m.
PSG want a deal worth at least £230m if they are to let Neymar leave, and have enquired about the possibility of taking full-back Nelson Semedo, in addition to Coutinho and the cash.
Barcelona do not want to lose Semedo, and have since suggested paying the full fee without including any players in the deal.
The club’s president, Josep Maria Bartomeu, is due to meet with PSG president, Nasser Al-Khelaifi, at the ECA summit this week where the discussions can continue.