The Reds had reportedly offered £8m for the Brazilian over the weekend, but this figure has been rejected by the Serie A side.
Anfield boss Brendan Rodgers is believed to be keen to add to his midfield options in a bid to further his team’s Premier League hopes.
He sees the 20-year-old as the ideal man to add some creative flair to his central options, and is prepared to convince the club’s owners to splash the cash.
It was thought that Tom Ince was the Merseysiders’ top target, but negotiations with Blackpool have hit a standstill in recent weeks, with the Seasiders unwilling to allow their star man to leave.
Rodgers may well return with an improved bid for Coutinho after missing out on Wesley Sneijder, but it is unclear if he will match Inter’s asking price, which is thought to be in excess of £10m.
The playmaker has struggled to make a significant impact on the San Siro outfit’s first-team and was loaned out to Espanyol last season.
However, they value him highly and believe that he has the potential to be a big star in the future.