Neymar is keen to be joined in Paris by his Brazilian team-mate and has urged his new employers to get a deal done ahead of his former club Barcelona.
Coutinho wanted to quit Anfield over the summer to force a move to the Nou Camp, but Liverpool held firm after insisting throughout the transfer window their star man was not for sale.
However, Liverpool’s viewpoint has not changed as the expect Barcelona to put in another offer during the summer.
Coutinho has only just recently established him back into the first team after a difficult summer which included him handing in a transfer request.
He has recently showed what an important player he is to Liverpool with three goals in his last three and despite having him under contract until 2022, they may be required to dig their heels deep once more to retain his services.