Despite signing a new long-term contract at Anfield in January, the Brazilian has been heavily linked to Camp Nou, even more so when it became clear that Neymar was leaving to join Paris Saint-Germain.
Liverpool manager Jurgen Klopp has reiterated numerous times that his star player is not for sale, but Coutinho himself is believed to be keen on moving to the Spanish club.
However, the 25-year-old will not force a transfer if the Reds cannot be persuaded to weaken their stance.
According to the Daily Mail, Barcelona remain hopeful that they will reach an agreement to sign the playmaker by the end of Tuesday after having a £72m bid and an offer in the region of £80m rejected.
The Catalan giants reportedly feel that Liverpool have accepted that Coutinho wants the deal to go ahead, and that a third bid will not be knocked back.