A Liverpool delegation flew out to Italy on Wednesday to negotiate the transfer of Inter playmaker Philippe Coutinho, Goal.comunderstands.
The Anfield officials, led by managing director Ian Ayre, are hopeful of agreeing a deal for the 20-year-old Brazilian.
But they face competition from Southampton, who have also declared an interest in capturing Coutinho.
Liverpool had a bid of around €7.7 million rejected for Coutinho last week but are confident an improved offer will be accepted by the Serie A giants.
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Inter have placed a valuation of €11-13m on the attacking midfielder, who has played a single full international for Brazil.
Coutinho’s public stance is that he is happy to stay at Inter but Liverpool have been given encouragement that a deal is possible this month, given the state of finances at the Italian club.
The player signed for Inter from Vasco da Gama when he was 16, though he spent a further two years at the Brazilian club before moving to Italy. Coutinho had a productive spell on loan at Espanyol in the second half of last season before returning in the summer to Inter.
Despite starting only three of the club’s Serie A matches this season – and making 10 league appearances in total – Coutinho is regarded as an emerging star.
Speaking to Sky Italia earlier this week about Liverpool’s interest, he said: “The Liverpool offer? I'm happy with these offers, because it means I am doing my job well.
"But I think Inter have faith in me and I want to show my value here. I don't feel that I'm on my way out. I hope to stay at Inter. The young players feel the faith of the coach and of the club."