The 20-year-old has agreed personal terms with the Anfield club and will be officially unveiled after securing a work permit and completing paperwork.
The Brazilian was pictured with his new club's shirt on Tuesday evening having stopped to sign it for a supporter.
Coutinho, who has one senior Brazil cap, has made just five Serie A appearances so far this term after finding himself down the pecking order upon his return from last season's loan spell with Espanyol.
Inter president Massimo Moratti recently described the midfielder's move to Anfield as a "great opportunity" for him to gain more playing time.
He is set to become Liverpool's second signing of January following the arrival of Daniel Sturridge from Chelsea.