The negotiations with the Merseyside club are already underway but Mundo Deportivo claims that sources at the Catalan club have admitted that Coutinho won't come alone if they lose Neymar to the Ligue 1 side.
The Liverpool ace was linked with a move to the Nou Camp earlier in the summer. The Brazilian typically plays as one of the forwards in Jurgen Klopp's 4-3-3 formation but it was said that Barcelona saw him as a potential long-term replacement for Andres Iniesta in midfield.
That speculation cooled when it emerged that the PSG star Marco Verratti was Ernesto Valverde's number one target to fill that role. However, Barcelona have revived the interest in the Liverpool ace in recent days after conceding a defeat in their attempts to sign the Italy international.
Reports in recent days have suggested that Coutinho could move to the Nou Camp to replace Neymar with the latter being tipped to make a €222m (£198.8m, $261m) move to the Ligue 1 side.
However, Mundo Deportivo journalist Miguel Rico, one of the best connected with the Catalan club, says that Barcelona will also try to sign a marquee forward if Neymar leaves.
Rico says that Barcelona openly admit that they are in negotiations over the signing of Coutinho after sending officials to London earlier this week in a bid to convince Liverpool to part ways with the player.
Mundo Deportivo then said Barcelona are preparing to launch a £80m offer to test Liverpool's resolve having already had a £72m bid rejected - while other sources claim the Reds won't negotiate his departure for less than £134m.
Yet, Rico claims the potential arrival of Coutinho has nothing to do with Neymar saga as the club were already planning to sign the Liverpool star before the prospect of Neymar leaving had even emerged.
With this in mind, the Mundo Deportivo reporter says that Barcelona have admitted that should Neymar leave, they will also launch a plan to add another world class forward to Valverde's ranks.
Rico says that Barcelona have failed to give any clue on who could be the chosen one but names Real Madrid target Kylian Mbappe, Juventus' Paulo Dybala and Borussia Dortmund's Ousmane Dembele as three potential candidates.
Mundo Deportivo says signing them would probably require an outlay of at least €100m but the Catalans could afford that fee, plus cover the cost of Coutinho's arrival, with the €222m they will would receive from the Neymar deal.