Barcola, 23, has become Liverpool's top priority to bolster the flanks in the closing weeks of the window, with the France international having told PSG he has no intention of extending his contract, which currently runs until 2028.
The winger has made clear he would prefer to join Liverpool over any other suitor, according to L'Équipe, which reported on Friday that the Merseyside club will formally offer just over €100m for the 23-year-old, with the exact figure put at €115m.
That opening offer is expected to be rejected by PSG, who are said to want closer to €170m to let their player leave, but it should nonetheless move negotiations into a more concrete phase.
The scale of Liverpool's interest is underlined by the fact that no other deal for a player in Barcola's position is currently as advanced, with the club having identified him as the priority option to add width and end product to Andoni Iraola's attack.
Barcola, formerly of Lyon's academy, has previously been described as frustrated with a rotational role under PSG head coach Luis Enrique, having been left out of both of the club's Champions League final wins.
Talks between the two clubs are expected to continue in the coming days as Liverpool look to bridge the gap between their opening offer and PSG's valuation before the transfer window closes.