Barca's second bid for the 25-year-old, which was rejected immediately, comprised an initial 85m euros (£76.8m) plus 15m euros (£13.5m) in add-ons.
Liverpool have reiterated that Coutinho - who joined them from Inter Milan for £8.5m in 2013 - is not for sale.
Barcelona sold Brazil forward Neymar to Paris St-Germain for a world record transfer of £200m last week.
Coutinho who scored 14 goals last term and spent six weeks out with an ankle injury, signed a new five-year deal in January, which did not include a release clause.
Manager Jurgen Klopp said the Reds were not "a selling club" when Barca's previous £72m offer was rejected in July, and Liverpool consider the matter closed.
Liverpool have rejected a bid of 100 million euros (£90m) from Barcelona for Brazil playmaker Philippe Coutinho.