
The Spanish giants already had an interest in Coutinho prior to Neymar's €222m transfer to Paris last week.
And Barcelona-based newspaper Sport reported a deal for the 25-year-old is "a question of hours" with Barca officials in England on Tuesday to thrash out a deal.
Both Sport and ESPN Deportes claimed Barca will pay an initial €90m fee.
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However, according to ESPN, bonuses could take the total value of the deal to €120m.
Barca believe the Brazilian international has the ability to not only replace Neymar alongside Lionel Messi and Luis Suarez in a star front three, but could also provide cover for 33-year-old captain Andres Iniesta in midfield.
Liverpool manager Jurgen Klopp told Barcelona "to save their energy" last week, claiming the player wasn't for sale.
However, he was left out of Liverpool's squad for a friendly win over Athletic Bilbao in Dublin at the weekend.
Coutinho already has La Liga experience on the other side of Barcelona as he enjoyed a successful six-month loan spell at Espanyol in 2012.
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He then joined Liverpool in January 2013 for just £8.5m.
In 182 appearances for the English giants, Coutinho has scored 42 goals.
He has also established himself as a regular starter for Brazil since Tite's appointment as coach last year, scoring seven times in 28 international appearances.
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