The 23-year-old has indicated he does not wish to sign a new contract at the European champions and is open to a move to Anfield, where Liverpool have held a long-standing interest. PSG are willing to sell but believe, given his age and potential, that £140 million represents a fair valuation, with Barcola having two years left on his contract.
Liverpool will look to negotiate a lower figure, with his price reported to have been closer to £75 million last summer when the club first made contact with his representatives.
Barcola is not a guaranteed starter under Luis Enrique, who has options including Ousmane Dembélé, Désiré Doué and Khvicha Kvaratskhelia ahead of him. PSG had been pursuing RB Leipzig's Yan Diomandé, a deal that would have pushed Barcola further down the order, only for Real Madrid to move decisively for the Ivorian, with that transfer now close to completion.
Liverpool had an £85 million bid for Diomandé turned down earlier in the window, but Barcola has remained part of their thinking throughout.
The winger's skillset is seen as well suited to Andoni Iraola's style of play and offers a direct goal threat following the departure of Mohamed Salah. Arsenal and Bayern Munich also retain an interest in Barcola, while Chelsea made enquiries earlier in the summer, though Arsenal are currently focused on exploring a move for Real Madrid's Vinícius Júnior and retain ambitions to sign Atlético Madrid's Julián Álvarez.
Barcola is understood to be keen to speak to Liverpool should they reach an agreement with PSG on a fee.
PSG's valuation would represent a club-record sale and comfortably surpass the British transfer record set by Chelsea's £117 million signing of Morgan Rogers this summer, underlining the scale of investment Liverpool would need to complete the deal.
Barcola impressed for France at this summer's World Cup, scoring three times as Les Bleus reached the semi-finals, form that has only strengthened PSG's belief in his value even as his club role remains uncertain.
With Liverpool determined to find a long-term successor to Salah before the window closes, the coming weeks look set to prove decisive in whether the two clubs can find common ground on a fee.