According to British media reports, the latest offer was worth £118 million (€129m) including £36.5 worth of add-ons, according to The Times. That follows two previous rejected bids from the Catalan side worth £72m and £90m.
Coutinho handed in a transfer request last week and has not featured in Liverpool’s first two games of the season due to a back injury.
Prior to the Brazilian’s request, Liverpool’s owners, Fenway Sports Group, released a statement saying saying “no offers for Philippe will be considered.”
The Reds after opening the Premier League season with a 3-3 draw away to Watford return to the pitch with a home game against Crystal Palace on Saturday.