Coutinho, 20, had been a target for Reds this month and if the deal goes through, he will be Brendan Rodgers second signing during this transfer window after Daniel Sturridge.
Inter are willing to sell Coutinho, who joined them at the age of 16, to raise funds for their Brazilian target Paulinho from Corithians. The Brazilian spent the last season on loan at Espanyol under current Southampton coach Mauricio Pochettino.
The young Brazilian was linked with Southampton after Inter reportedly agreed a £10million bid from the Saints.
However, Liverpool have been snubbed in the past during the summer transfers with Gaston Ramirez joining Southampton while their long-term target Tom Ince is still in talks for a return to Anfield.
Rodgers is need for reinforcements in his squad after falling short of strikers but the signing of Sturridge, Fabio Borini's recovery from injury in added boost for the Reds.
Liverpool are currently seventh in the league with 34 points, three points below next week's opponents Arsenal.
Meanwhile, Rodgers could be forced to send defender Sebastian Coates on loan or sell him to Brazilian club Gremio. Liverpool are plotting a move for Swansea defender ashley Williams in the summer but face competition from Arsenal.