Neymar's transfer will be concluded "within 44 hours", according to Mundo Deportivo.
Barcelona and PSG's presidents; Josep Bartomeu and Nasser Al-Khelaifi, will meet in Liverpool to finalise the Brazilian's transfer.
The pair will try to reach an agreement on the Brazilian.
Barcelona's opening bid for Neymar failed, as PSG rejected an offer of £74million plus fellow Brazilian, Phillipe Coutinho.
The French champions are demanding more cash and more players for Neymar, who they broke the world record fee for in 2017.
PSG want the £206million they paid for the forward back in full if he is to leave the club.
Real Madrid are also interested, and Al-Khelaifi is thought to prefer Neymar leaving for Madrid than Barcelona.
But Neymar is said to prefer a return to the Nou Camp.
The Brazilian international posted a picture of himself with Madrid boss, Zinedine Zidane, on social media last week, fuelling speculations on his future.