The Reds named their 25-man squad for the tour match with the mercurial Brazilian the biggest ommision, while German midfielder Emre Can will also miss the trip Down Under.
The pair are expected to join their international teammates with Can's Germany side taking part in the Confederations Cup and Coutinho's Brazil team to take on the Socceroos and Argentina at the MCG on June 9 and June 13.
Despite Coutinho not being named, Liverpool has announced a near full strength squad including captain James Milner, Joel Matip, Roberto Firmino, Adam Lallana and Daniel Sturridge.
As was announced by the club earlier this month, former Liverpool greats Steven Gerrard, Daniel Agger Jamie Carragher and Steve McManaman are all expected to play after being named in Klopp's team for the match.
Jordan Henderson will miss the trip as he continues his recovery from a foot injury.
The match will take place only two days after Jurgen Klopp's side wrapped their Premier League campaign with a 3-0 win against Middlesbrough
