The Reds have already turned down three offers for the Brazilian, worth £72 million, £90.4 million and £114.2 million respectively.
The last of those bids was reported to be worth £118 million (128.7 million euros, $151 million), but Liverpool have maintained their stance that the 25-year-old will not be sold in the current transfer window, which shuts at the end of August.
Sportsmail understands the Brazilian is yet to give up hope of sealing a dream move to Spain, despite Liverpool manager Jurgen Klopp insisting on Tuesday that he is ready for Coutinho to return to the squad once he recovers from a back injury.
Despite Coutinho handing in a transfer request, the Anfield club reportedly informed Barcelona that they do not want any more contact from them after rebuffing a third offer, said to include unrealistic add-ons.
According to Sky Sports News, Barcelona will make one final effort to secure the player despite suggestions they had given up the chase.
Balague suggests that the Spanish giants are fully aware that Liverpool will reject their final £128.8m offer but they are submitting it to appease Coutinho and are now focussing their attention on signing Ousame Dembele and Angel Di Maria instead. "Yes, indeed, absolutely, 100%".
Liverpool are two games into their Premier League season and face Hoffenheim in the second leg of their Champions League playoff clash on Wednesday and Coutinho has missed all the games thus far due to a back injury.
Klopp revealed that Coutinho is also suffering from a sickness bug and is unsure when he will return.
"If [Coutinho] would start [training] tomorrow it would take time because he has no training for a long time".
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