Coutinho is due to travel to Merseyside in the coming days to discuss personal terms and undergo a medical ahead of the move.
Liverpool faced competition from Southampton for the Brazilian but appears to have got its man after an Anfield delegation flew to Italy this week to negotiate the transfer.
The Reds have increased their initial 6.5 million pound bid for Coutinho and the 20-year-old is understood to have made clear his preference to move to Anfield.
Coutinho played under new Southampton manager Mauricio Pochettino while on loan at Espanyol last season but Liverpool manager Brendan Rodgers has been determined to improve his squad as he targets a top four finish.
The Reds signed Daniel Sturridge from Chelsea at the start of the month in a 12 million pound deal and are also hoping to conclude a move for Blackpool midfielder Tom Ince before the transfer window closes at the end of the month.
They will have to apply for a work permit before Coutinho’s proposed transfer can be concluded but that is regarded as a formality for the versatile playmaker, who has been capped once for Brazil.
Inter’s financial circumstances have seen the team actively encourage Liverpool’s interest in Coutinho this month, despite selling Wesley Sneijder to Galatasaray, as the Serie A giants line up a move for Corinthians star Paulinho.
Coutinho 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."