The most recent offer, worth £118 million, followed two of £72m and then £90m, with Philippe Coutinho handing in a transfer request and missing Liverpool's first two Premier League games of the season.
For more on Coutinho to Barcelona, as well as other rumours, check out Transfer Talk by clicking here.
Liverpool's narrow 1-0 win over Crystal Palace on Saturday saw several changes to what's regarded as their first-choice team. Jurgen Klopp selected the same XI for the Reds' opening two games, so alterations on Saturday were the first glimpse of how they'll manage when reserve players have to be selected.
Many fans feel like Klopp hasn't done enough to deepen his squad, although others blame the owners and a volatile, ludicrously inflated market. Victory camouflages all ills and while Klopp was...
It's been only seven months since a smiling Philippe Coutinho posed for photographs alongside Liverpool manager Jurgen Klopp after signing a new five-year contract at Anfield.
"I signed this new contract to stay here for a few more years because it's a great honour for me," Coutinho said at the time. "It gives me great happiness because I was welcomed here with open arms by everyone at the club and the supporters right from my first day.
"I am very thankful to this football club for everything."