The Catalan giants had a £72m bid rejected last week, with Liverpool boss Jurgen Klopp insisting that the 25-year-old was not for sale and that Liverpool "are not a selling club".
However, Spanish publication 'Sport' reports that the Merseysiders have placed an £89m valuation on the Brazilian's head and that Barca are seriously considering paying it.
The same source claims that Barcelona are expecting to sit down for talks with both senior Liverpool officials and Coutinho's agent in the near future.
The Brazil international enjoyed a fine season last time out, scoring 13 goals and providing 7 assists in 31 Premier League games and attracting plenty of admiring glances in the process.
At this point, it is unclear whether the move for Coutinho relies on Neymar leaving for PSG or, as has been speculated, whether the move for Coutinho is an attempt to convince Neymar to stay, with the pair enjoying a close bond.
Alternatively, 'The Daily Mail' suggests that Coutinho is seen as the long-term successor to Andres Iniesta at the Camp Nou, though it also states that any move is likely to be a long, drawn-out affair.