Liverpool's opening bid for the 23-year-old has been rejected by PSG, according to RMC Sport, though talks between the two clubs are ongoing and an improved offer is expected to follow.
No figures have been made public for either the rejected bid or PSG's valuation of the player.
Barcola and fellow forward Ibrahima Mbaye were both left out of PSG's squad for Sunday's league fixture at Rennes, with manager Luis Enrique choosing not to consider either player until there is greater clarity over their futures. The transfer window closes on 1 September, meaning the situation is likely to be resolved one way or the other within days.
Liverpool are also weighing a move for the 18-year-old Mbaye, a Senegal international, though PSG's valuation of around €70 million for the teenager is well beyond what Liverpool are currently willing to pay.
With neither player currently in Luis Enrique's plans, a move away from Paris looks increasingly likely for at least one of the pair, and Liverpool are expected to table further offers for Barcola specifically in the coming days as they continue to strengthen their attacking options under Andoni Iraola.