Coutinho has emerged as a top target for Barca as they look to replace Neymar, after his €222 million (A$332.46 million) switch to Paris Saint-Germain.
The Reds are reported to have turned down two bids from the LaLiga giants, the second worth an estimated £100 million (A$164.77 million), and Fenway Sports Group - Liverpool's owners - released a statement on Friday insisting that further offers for the Brazil star would not be considered.
However, just a few short hours later, it emerged that Coutinho had reportedly demanded a departure from Anfield.
The move will boost Barca in their attempts to replace Neymar, after seeing a bid for Borussia Dortmund winger Ousmane Dembele rejected on Thursday.
The France winger was sanctioned by Dortmund for failing to report for training on the same day.
Coutinho will be out of action this weekend when Liverpool begin their Premier League campaign against Watford due to a back injury.
He scored 13 goals and assisted seven more in 31 Premier League appearances last term, helping Jurgen Klopp's side finish fourth.