The Brazil international has established a reputation as one of the Premier League's top creative talents over the past few seasons.
And he's long been linked with a move to swap Anfield for the Nou Camp as a potential long-term replacement for veteran playmaker Andres Iniesta.
Barcelona's interest in getting Coutinho on-board has escalated in the wake of Neymar's world-record departure to Paris St-Germain two weeks ago.
And Liverpool have so far knocked back three offers for the 25-year-old - the most recent of which came in before Saturday's 1-0 win over Crystal Palace.
Barcelona's bid on Friday night could have reached £118m, but only £80m of that was guaranteed.
And it was rejected out of hand by Fenway Sports Group (FSG), who insist they are desperate to keep hold of Coutinho.
The Sunday Express reckon Liverpool would considering selling the former Inter Milan ace for £140m though.
And Barcelona are apparently poised to test their resolve to not let him leave by lodging an offer of £130m.
The Sunday Express indicate that prospective deal would need to involve the La Liga giants stumping up more of the fee up front.
And it may see a revised payment structure proposed, with the guaranteed £80m previously offered being staggered over five years.
Coutinho handed in a transfer request earlier this month in an attempt to force his way out of Liverpool.
The fact he's under contract until 2022 means the Reds are under no pressure to sell him ahead of August 31's 11pm transfer deadline though.
