Barcelona-based daily SPORT said the two clubs had struck an ‘agreement in principle’ for the transfer of Coutinho worth 120 million euros ($144.34 million) plus 40 million euros in add-ons that would see the player sign a five-year contract.
That fee would eclipse the 105 million euros Barca paid Borussia Dortmund for France forward Ousmane Dembele in August.
It would also see Coutinho become the second most expensive footballer ever behind compatriot Neymar, who moved from Barcelona to Paris St Germain for 222 million euros in August.
The AS newspaper said Coutinho, 25, was expected to watch the La Liga leaders play Levante on Sunday in the presidential box at the Nou Camp, with a deal being made official next week.
Daily Mundo Deportivo also reported that Coutinho’s transfer to the Catalan club was imminent.
Neither club was immediately available to comment.
The Brazilian has not played in Liverpool’s last two games against Burnley in the Premier League and Everton in the FA Cup, with coach Juergen Klopp saying he has a thigh injury.
British media reported that Coutinho was also absent from the club’s trip to Dubai on Saturday for warm weather training.