There had been strong suggestions in the British and Spanish press in recent days that Coutinho would become a Barcelona player before the window closes, even as soon as this week if the La Liga club got their way.
Barcelona are understood to have fallen short with their initial bid earlier this week, while their latest approach – totalling over £90m with add-ons – was also knocked back.
The Catalan giants are desperate to bring in new faces to replace influential forward Neymar , who departed for Paris Saint-Germain last week in a whopping £198m deal.
Coutinho is widely considered to be the man Ernesto Valverde wants to fill that big attacking void, but opposite number Jurgen Klopp has constantly reiterated that no sale will go through this summer.
Sky Sports News reports that Barcelona’s latest offer included an initial fee of £76.8m upfront and £13.6m in further payments if various clauses were met.