However, Sky Sports News understands that there is a significant gap in valuation between the two clubs.
The Champions League holders value the 23-year-old at £145m.
PSG's stance on the fee makes it a difficult deal to complete at this stage.
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The Reds have also held preliminary talks with Barcola's representatives.
Signing a winger has been a key area to strengthen for Liverpool since the departure of Mohamed Salah, and Barcola has been on Liverpool's radar for a number of years.
The France international has two years left on his PSG contract and has indicated he will not be signing a new one amid frustrations at a lack of game time.
The opportunity to join Liverpool is said to appeal to the ex-Lyon forward.
The key to getting any deal moving will be PSG's willingness to reduce the price tag on the man they bought for around £40m back in 2023.
The success of Andoni Iraola's teams at Bournemouth and Rayo Vallecano centred around the pace, energy and work-rate from his wingers, so Barcola could be a key piece of the Spaniard's new Liverpool jigsaw.
The fact that Barcola has won nine major trophies in the last two years, including two Champions League titles, shows the calibre of player they are trying to bring to Anfield.
Arsenal, who missed out on signing Vinicius Junior following his Real Madrid contract extension, also hold an interest in Barcola.
