Barca have already seen two bids turned down for Neymar, who left the club for France in a world record €222 million transfer in 2017.
PSG rejected a first offer which included Philippe Coutinho, Ivan Rakitic and €80m and then dismissed their request to take him on loan this season ahead of a permanent move next summer in a deal which would have been worth around €190m.
With less than two weeks to go before the transfer window closes on Sept. 2, Barca are against the clock to come up with an offer which suits PSG.
The French champions could set a deadline for any potential deal, too, as they want to have their squad finalised as soon as possible.
Barca's next offer, therefore, could be their last. The club's hierarchy are not in complete agreement over a move for Neymar but are working on a formula which they hope will finally secure Neymar's Camp Nou return.
Barca have insisted this summer that Dembele would not be used in a potential deal but sources inside the club have told ESPN FC that stance has softened.
Despite Dembele's agent, Moussa Sissoko, saying earlier this week that the France international will remain in Catalonia, they are now thinking about offering him in a player-plus-cash deal.
Coutinho's agent also suggested he would remain at Camp Nou days before his move to Bayern Munich last week, which meant he was not included in Barca's bid to re-sign Neymar.
There is disappointment about how Dembele, who was ruled out for over a month earlier this week, has handled his latest injury. He didn't tell the club's medical staff about the full extent of the problem after last Friday's loss to Athletic Bilbao and it wasn't until the Monday that the club realised the severity of the damage to his hamstring.
Sources have told ESPN FC that PSG coach Thomas Tuchel, who worked with Dembele at Dortmund, would love to be reunited with the forward but the club's sporting director, Leonardo, has doubts.
He is concerned about the number of Barca games he has missed through injury -- the latest of which means he won't be available for action until October.
There's also interest in Neymar from Real Madrid and Juventus, although neither club has yet to make an official bid. Despite that, Barca believe that every outcome remains possible and are not ruling anything out.
Neymar has told PSG that he wants to leave this summer and the Ligue 1 side want to recoup a majority of the fee they paid two years ago.
Sources say they believe they are in a strong position to negotiate because it was never their intention to sell a player who is under contract until the summer of 2022.
If no satisfactory offer arrives, they will look to reintegrate Neymar into the first team. He has not played since injuring his ankle in Brazil's Copa America warmup against Qatar at the start of June.
ESPN FC's Julien Laurens contributed to this report.