PSG had originally quoted suitors a price of around £145m for the 23-year-old, but The Times reports a deal could now be struck for something closer to £115m.
That figure would provisionally make Barcola the second most expensive signing in Liverpool's history, behind only the British-record £125m the club paid Newcastle for Alexander Isak last summer.
Any deal for Barcola would form part of a broader spending spree across the Premier League that could reach beyond £1bn in the closing fortnight of the window alone, according to the Telegraph.
Several transfers have already touched or breached the £100m mark this summer, including Elliot Anderson's move to Manchester City and Morgan Rogers's switch to Chelsea, while others remain under negotiation — Enzo Fernández has been linked with a move to City, and Arsenal are locked in a battle to sign Julián Álvarez, quoted at over £100m.
Nicolas Jackson's £65m switch to Aston Villa, though a club-record fee for Villa, looks comparatively modest set against those numbers.
Barcola has been a target for Iraola's Liverpool since the early weeks of the window, with Mikel Arteta's Arsenal also weighing up a move to strengthen their own wide attacking options.
Liverpool had two earlier approaches turned down by a PSG hierarchy previously insistent the winger was not for sale, with Barcola himself said to favour staying in the French capital at that stage, but the mood around a deal has since shifted as his contract situation has become clearer.
The France international impressed at this summer's World Cup, scoring three times despite frequently being used as an impact substitute, and played a significant role in PSG's back-to-back Champions League triumphs, adding further weight to the case for a fee approaching Liverpool's transfer record.