The Brazil international has been pursued by the Blaugrana all summer, but the Reds have publicly declared that they do not want to sell their star player.
On Friday, Sky Sports News reported that Liverpool rejected a third bid from Barca, believed to be in the region of £113m, and it has now been claimed that the Catalans are close to conceding defeat.
Balague said: "We reported on Friday that Liverpool had rejected the third offer from Barcelona and an email was sent back [to Liverpool] from Barcelona saying, 'okay, you rejected that - if you don't accept it I must tell you that there is a deadline of today, Sunday - 7pm. Otherwise we withdraw the offer.'
"I think Liverpool have got no intention of answering that email from Barcelona, which in theory means that's the end of that. That's the end of the story of Coutinho moving to Barcelona.
"You never know in football of course but if Barcelona are true to their word they will withdraw the offer tonight because Liverpool have got no intention of selling."
Coutinho, whose most recent appearance for Liverpool came in the 3-0 friendly win over Hertha Berlin on July 29, scored 13 goals and set up a further seven in the Premier League last season.