Elsewhere, World Cup semi-finalists Jordan Henderson, Simon Mignolet and Dejan Lovren are all yet to return to training and will be absent - although Trent Alexander-Arnold, who came back early, could play some part.
And suffice to say that some Liverpool fans are already loving what they have seen from the powerful midfielder, who came off after 70 minutes.
Jurgen Klopp has handed new signing Alisson Becker his debut as the Brazilian global goalkeeper starts between the sticks against the Serie A giants while Nathaniel Clyne, Joe Gomez and Andrew Roberton join Virgil van Dijk in defence.
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The interplay between the front-three was also impressive.
It also looks like Liverpool have some much-needed strength in depth for the season ahead.
And Virgil Van Dijk made sure to show his appreciation to Alisson for starting off the move. Liverpool's last was the League Cup triumph, way back in February 2012. Xherdan Shaqiri replaced Firmino at half-time and played nearly as a false-nine, dropping deep and looking to pick out the runs of Salah and Firmino.
With both sides throwing on substitutes in the second half, the game lost its rhythm, but Liverpool's superiority was unmistakable before Sturridge added a fourth, and Alberto Moreno a fifth with a vicious strike.
"The club will announce Alisson's permanent number in due course, and that of fellow summer signing Fabinho, who has provisionally been wearing No.3 in pre-season".