It is the third bid Liverpool will be knocking back from the Spaniards after offers of £66m and £90m were rejected for the Brazilian.
Liverpool have insisted that they will not sell Coutinho at any price, with the club’s owners, the Fenway Sports Group, releasing an official statement to that effect.
Coutinho, 25, is however determined to leave Anfield, where he arrived at for around £8m four years ago, and he has submitted a transfer request.
Coutinho participated in pre-season with Liverpool but he has missed the first two games of Liverpool’s season with a back injury: the Premier League draw at Watford and the Champions League play-offs win at Hoffenheim.
Barcelona are keen to strengthen their squad after selling Neymar to Paris Saint-Germain for €222m.