The Catalan giants have been on the trail of the Reds midfielder since last summer, but failed with three bids despite Coutinho submitting a transfer request to force through a move to the Camp Nou.
Liverpool are said to have softened their stance after learning that the midfielder remains keen on joining the La Liga side, but the two clubs remained at loggerheads with regards to the fee. It was being reported that Merseyside club were holding out for a fee of around €150m (£133m), while Barcelona were only willing to stump up around €130m.
The Spanish club seem to have loosened their purse strings further as according to The Telegraph, Ernesto Valverde's side have now upped their offer and are ready to pay Liverpool a fee of around £140m, including add-ons, making Coutinho the third most expensive player behind Paris Saint-Germain duo Neymar and Kylian Mbappe.
The Brazilian moved from Barcelona last summer after the Ligue 1 club met his £198m release clause after which they completed a loan move for Mbappe, which will become permanent this summer for a fee of around £166m.
The current La Liga leaders are desperate to complete the deal as early as possible during the ongoing January transfer window and the report claims that the representatives are in talks over a move. Barcelona are expected to pay £105m upfront with the further £35m being paid in add-ons with respect to appearances and successes achieved by Coutinho at the Camp Nou.
Liverpool remain reluctant to allow the midfielder to leave midway through the campaign and have made a last ditch effort to convince him to stay, but it remains unlikely as Coutinho is said to be keen to join Lionel Messi and co. at Barcelona this month.
Jurgen Klopp was asked about a potential move during his pre-match press conference on Thursday (5 January), the German manager refused to address it, but failed to deny that a move was a possibility. "I am not interested in Barcelona. Sorry. What can I say about what they do?" Klopp said, as quoted by the Telegraph.
"It is always the same. This year it is Phil. Another year it is somebody else. There is nothing to say until there is something to say. That is my position. What can I do? I cannot talk about this part of the game. You discuss it but we cannot be part of the discussion. You can write what you want, you can interpret whatever I say," the German coach added.
Liverpool have been linked with a move for AS Monaco midfielder Thomas Lemar, who they view as a perfect replacement for the Brazilian. They will, however, face competition from Arsenal and Chelsea if he is made available for transfer, which according to the Ligue 1 club's manager will not happen in January.