The 23-year-old scored 11 goals and added one assist in 29 Ligue 1 appearances last season, 21 of them starts, for the reigning European champions.
Liverpool and Barcola's camp are understood to have already settled personal terms, and the two clubs have also closed in on a fee in the region of €125m (£110m), according to journalist Nicolò Schira, with PSG having originally demanded closer to €170m.
Barcola has been strongly linked with several of Europe's biggest clubs this summer, including Arsenal, though Liverpool have emerged as the party furthest down the road with PSG.
The France international is under contract in Paris until the summer of 2028, but reports suggest any move to Anfield would see him sign fresh terms running until 2032 — a six-year commitment reflecting Liverpool's view of him as a long-term fixture rather than a short-term fix.
Liverpool have been searching for attacking reinforcements since Mohamed Salah's free transfer exit to Trabzonspor, with the club also monitoring developments around Hugo Ekitike's long-term injury layoff.
Barcola would give manager Andoni Iraola a direct, pacey option on the left of an attacking line that has looked for fresh legs following Salah's departure. Liverpool have previously seen a bid in the region of €120m rejected as PSG held out for a fee closer to their original €170m valuation, with the gap between the clubs narrowing steadily over the past fortnight.
Barcola was left out of PSG's matchday squad for their European Super Cup win over Aston Villa last week, a decision widely read in Paris as a sign the club are preparing for his departure.
The club are bringing in Ferran Torres from Barcelona as a potential replacement in the forward line, further easing the path for Barcola to leave. Talks between the two clubs have moved quickly in recent days, though the final figure — and whether add-ons are included in the reported €125m fee — has not been confirmed by either party.
Should the deal go through, it would rank among the biggest incoming transfers of Liverpool's summer business, comparable to the fee they paid Newcastle for Alexander Isak a year ago.