Spanish publication Sport claims the Merseysiders have softened their stance after Coutinho's agents recently met in Boston with representatives of Fenway Sports Group to make it clear that the Brazilian ace still wants a move to the Nou Camp.
Coutinho, 25, only signed a new deal, reportedly worth around £150,000-a-week, in January to become the highest-paid player at Liverpool.
However, the Brazilian tried to force a move to Barcelona during the summer after being identified as a top priority for Ernesto Valverde's side.
The Spanish giants launched multiple offers to complete the move, but eventually opted against matching the €200m (£176m) demands made by Liverpool.
Last week Barcelona president Josep Maria Bartomeu suggested that the club would not make a new attempt to sign him in January.
"Right now there is nothing planned for the January window. [Technical secretary] Robert Fernandez, [sporting football manager] Pep Segura and their team will work to see if they believe it is necessary to do something," Bartomeu said when to TVE when asked if Barcelona will make a new attempt to sign the Liverpool star ahead of the second part of the season.
"I will not say how much we offered, but they asked for €200m. We weren't going to give €200m or €150m – we decided to step away from such an expensive market, our offer was less than €100m, with add-ons it could have reached €120m."
However, Sport claims that Barcelona are still working with Coutinho's entourage in a bid to complete the move during the coming January market – or at least in the summer.
Indeed, the Spanish publication says the Catalans are more optimistic than ever, with Liverpool being finally open to parting ways with the Brazilian ace for a reasonable prize.
The report says Liverpool refused to negotiate the departure of Coutinho during the summer in the hope that the Brazilian could help Jurgen Klopp's side to battle for the Premier League title this season.
However, the Fenway Sports Group have softened their stance following an inconsistent start to the season, with Liverpool being sixth in the Premier League table, five points behind Manchester City and Manchester United.
Coutinho would be cup-tied for Champions League games after he recently played for Liverpool during the recent 2-2 draw with Sevilla. However, Sport says that the player's entourage expects this to not hamper any move as the Brazilian is still determined to join Barcelona.