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Rodgers is in advanced negotiations with Inter over a deal to sign the Brazil international and Liverpool expect to seal their second January signing by the end of this week.
Liverpool's first bid was rejected last week but they are ready to offer a £6 million down payment with further instalments taking the transfer closer towards a final £8 million.
Talks between the two clubs resumed on Monday and barring any late hitches, Coutinho should join Daniel Sturridge as the latest arrival at Anfield this month.
Coutinho's versatility appeals to Rodgers, the Liverpool manager, as he can play in central midfield and as a second striker.
The 20 year-old was signed from Brazilian club Vasco da Gama and given his first-team debut by former Liverpool manager Rafael Benítez and has established a reputation as one of Serie A's most prodigious young talents.
His age also fits the profile for Rodgers, who could still move for Blackpool and England U21 international winger Thomas Ince before the transfer window closes next week.