Brazilian ace would earn £237,000-a-week if he completes the move to the Nou Camp.
Sport claims that the La Liga giants need to part ways with three players to balance their books.
Coutinho was already poised to move to Barcelona in the summer.
Sport claims that the club chief himself will lead the negotiations to seal a mega-money deal which is expected to be extra complicated due to both the demands of Merseysiders and Coutinho's own salary purposes.
The Spanish publications claims that Barcelona plan to launch an initial offer worth €130m (£114.7m, $155m) to test Liverpool's resolve while the Brazilian international wants €14m a year in wages to complete the transfer – equivalent to €269,000-a-week (£237,000-a-week).
Sport adds that the La Liga giants would need to part ways with up to three stars from Ernesto Valverde's current squad in order to fulfil their financial regulations regarding the player's salary.
The widely-expected departure of Arda Turan could pave the way to sign Coutinho with the Turkey international currently earning €8.5m-a-year despite not having played a single game in the opening part of the season.
However, Sport says that Barcelona would still need to show the exit door to two more players to give the Brazilian ace the €14m they already agreed to pay him in the summer before the negotiations with Liverpool collapsed.
Sport claims that Barcelona are still more optimistic than in the summer as Liverpool are now willing to cash in on with the player for the right price.
Earlier this week Sport said that Coutinho's agents had managed to soften the stance of Liverpool's owners Fenway Sports Group during several meetings held in Boston after in the summer they made it clear that the player was not for sale.
The Spanish Publication reported that Liverpool would be willing to sanction Coutinho's departure in January if Barcelona return with an offer worth a total of €150m with add-ons.
The new information from Sport claims that Bartomeu plans to launch a first offer worth €130m to test Liverpool's resolve but the Barcelona president is well aware that the deal could end up costing €150m.
In the summer, the La Liga giants already broke the bank to sign Ousmane Dembele from Borussia Dortmund in a club record deal worth €105m plus €40m in add-ons. And Sport claims that Barcelona are ready to go beyond that fee to sign the Liverpool ace.
"We are prepared to sign Coutinho or other players but the proposal has to come from the technical staff. We will do our best to meet their demands," Grau said during a press conference in which he revealed a club record budget for the 2017-2018 campaign of €897m.