British media reports said Barcelona’s latest bid was worth around £114 million ($146.5 million, 124.7 million euros), a significant increase on their previous offer of £90 million.
Liverpool have publicly stated that Coutinho is not for sale at any price and consider the figures being offered by Barcelona irrelevant.
The 25-year-old Brazil playmaker, currently sidelined by a back problem, has submitted a transfer request.
He signed a new five-year contract in January.
Barcelona have targeted Coutinho and Borussia Dortmund winger Ousmane Dembele to plug the gap created by Neymar’s world-record 222 million euro ($260.8 million) move to Paris Saint-Germain.
Speaking on Thursday, Barca general manager Pep Segura said deals for the pair were “close”.
But Liverpool are refusing to budge and Dembele, 20, has been suspended by Dortmund after going on strike in a bid to force through a move.
Coutinho joined Liverpool from Inter Milan in an £8.5 million move in January 2013 and is the key creative figure in Jurgen Klopp’s team, scoring 14 goals in all competitions last season.