Multiple media outlets in both Spain and England claim the 25-year-old believes he has played his last game for the Reds and is pushing for a move to the Nou Camp in the January transfer window.
Reports earlier this week via Mundo Deportivo and Sport said that Barcelona were lining up a total offer worth €150m (£132.94m, $180.27m), though Liverpool insist they are yet to receive a bid.
A meeting between officials from Liverpool and Barcelona is scheduled for this week when a deal could be thrashed out, and while negotiations are ongoing Coutinho has no plans to play for the Merseysiders.
But should the saga enter the second week of the January window then Coutinho will refuse to play for Liverpool against Manchester City on 14 January, to ensure further injury does not derail his dream of moving to the Catalan giants.
Jurgen Klopp, the Liverpool manager, has steadfastly refused to openly discuss the subject of Coutinho's future, but with the club having yet to confirm he is not for sale in this window there are suggestions they are open to entering into discussions with the La Liga leaders.
However, former defender Jamie Carragher believes Liverpool would be foolish to part ways with the one-time Inter Milan man and feels a deal in the summer would suit the Anfield club better.
"Best thing [for] Liverpool is agree the BIG fee for Coutinho to go in the summer like we've done with [Naby] Keita, not now," Carragher, Liverpool's second highest ever appearance maker, wrote on Twitter.
"What do the club gain by doing it now? Top four and Champions League progression seriously risked if they sell in January, and difficult to replace him now. If he goes on strike he damages himself."