Liverpool have insisted over the last few months that the Brazilian star is not for sale, especially as he signed a new five-year deal at Anfield in January.
Barcelona have not contacted Liverpool since their initial £72 million bid was firmly rejected, but Valverde's side are prepared to bump up the offer in their search for alternatives after Neymar's exit.
And, according to Sky Sports, Coutinho is also keen on a move to the Camp Nou, as long as the deal can be done amicably with Liverpool.
The Brazilian will not try to force through a move to Barcelona, but he is interested in playing alongside Messi and Suarez. The Catalan club is the only destination Coutinho is considering, but it all seems to be down to Liverpool now.