The La Liga giants had three failed bids for Coutinho, the highest being £114m, and are said to be already negotiating a January move.
Coutinho's performances will have done nothing to deter Barcelona, and according to the Times' Paul Joyce, they are likely to make another bid in the winter transfer window.
It's stated that an agreement is already in place for Coutinho to join Barcelona should the clubs come to an agreement, which could be a hard objective for the La Liga leaders, as Liverpool still hold Coutinho in extremely high regard.
Sport also report that Coutinho has asked Liverpool and his advisors to ignore any offers that come from PSG.
'Despite trying to leave Liverpool he continued helping the team and working.
Sport reports the Blaugrana will make a new €120 million (£106m) offer for the Brazilian, who is now nursing a calf problem.
Sport are now so confident of Coutinho leaving Liverpool for Barcelona in January that they claim the main issue between the two clubs is how to divide the payments.
Coutinho and Barcelona came to an understanding in June on a five year contract, and the Catalan newspaper say that's being stuck to.
"I know him as a person and as a player because I played with him, but everyone knows what Coutinho can contribute".
"No player has retired at Barca because it is very hard and very complicated".
Philippe Coutinho is now with the Brazil squad preparing for friendly matches against Japan and England.