The Spanish giants bid €100m (£90.2m) for the playmaker but it was rejected out of hand and Barca fear the Reds will hold firm in their stance that the Brazilian is not for sale at any price.
Sporting director Robert Fernandez is willing to be patient in his pursuit of Coutinho and the club do appear to have a misplaced confidence that this deal will get done when it is becoming increasingly obvious that Liverpool are ready to shut down any attempt at opening talks. The €100m offer would have made the Brazil international one of the most expensive players of all time but the Reds wasted little time in turning down Wednesday's bid.
Coutinho is understood to be open to the prospect of moving to the Nou Camp, keen even, but those close to Liverpool do not expect the 25-year-old midfielder to force the issue.
Without such action from the player it is looking increasingly likely that a tough summer for Barcelona will be further frustrated.
After failing in their bids for Hector Bellerin and Marco Verratti, Barca lost Neymar against their will as Paris Saint-German activated his release clause.
It means they have €220m (£200m) from that transfer burning a hole in their pocket but the whole world knows it and Borussia Dortmund, the club of another Barca target Ousmane Dembele, are ramping up their asking price in response.
Dembele is now being valued close to €150m by the Bundesliga outfit, making a double deal difficult in a summer when Barcelona know they must make a big signing to save face after Neymar's exit.
Whether it will be Coutinho, the PSG man's compatriot, looks set to depend on whether the playmaker is ready to tell Liverpool he wants a move away from the club.
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