The report stresses that there are still details to finalise, but that Liverpool have reached an agreement in principle with the reigning Champions League winners.
The Athletic have stated that there will be a fixed fee of 100 million euros (£85.8m), plus a further 20 million (£17.1m) in add-ons.
Barcola joined PSG from Lyon in 2023 and has been a huge success for the Ligue 1 powerhouses, making 152 appearances, scoring 39 goals and registering 37 assists.
The Frenchman won several trophies in Paris, including three league titles, two Champions Leagues and two French Cups.
His form also saw him break into the French national team and feature at the 2026 World Cup, where he found the net against Senegal, Sweden and England.
The 23-year-old would become Liverpool's fourth summer signing after the arrivals of Jeremy Jacquet, Victor Munoz and Ronald Araujo.