The Brazilian is wanted by the Spanish giants to replace Neymar – who joined PSG for £199million.
But according to Le Parisien , the French side are not ready to stop spending yet, and could launch a £100million bid for Coutinho.
PSG want to build a team that can win the Champions League and are prepared to spend big money to fine tune their squad.
But all of Barcelona’s approaches for Coutinho have so far been rebuffed with Jurgen Klopp insisting none of his star players will be sold this summer.
The situation is likely to be the same with any approaches from PSG.
Coutinho was left out of the Liverpool squad on Saturday night for the friendly against Athletic Bilbao.
The 25-year-old is still suffering from a slight niggle that also saw him miss the meeting with Atletico Madrid.
Klopp, meanwhile, has effectively admitted defeat in the hunt for Vigil van Dijk. The German manager has revealed he will not sign a new defender this summer.
“We have four centre-backs. I don’t think we need more,” Klopp said. “Just at the moment I’m fine. The transfer market is open until the 31st of August.
“We cannot force things and we would never get a centre-back just because someone is available.
“Look out there and tell me five that would make us stronger. Then you win a prize! It’s difficult. I’m happy. You can imagine we still work on different things and we will see if it works.