This will be the first competitive encounter between Maribor and Liverpool.
Alex Oxlade-Chamberlain though, would be itching to receive the elusive start, while Philippe Coutinho and Mohamed Salah are unlikely to be rested for what is a highly important game.
Things did not change for the hosts as the second-half was as routine as the first for the visitors.
Maribor have had a tremendous start to the Slovenian League.
Klopp'sdecision to bring Milner back into the starting eleven was immediately repaid with the Englishman's service in the second goal truly magnificent.
The in-form Egyptian got a brace in the 40th minute after Alberto Moreno sprayed a pass and he had an easy job to slot the ball into an empty net, making the scoreline 4-0.
The Reds, who had drawn their opening Champions League games, were under pressure to beat the minnows but once they raced into a 3-0 lead inside twenty minutes, the result was never in doubt. It was the first time the Reds had netted seven times away from home in Europe and Klopp, whose team had been on an indifferent run, said: 'The attitude was outstanding - were spot on from the first second.
Mohamad Salah was delighted with the way Liverpool destroyed Maribor on Tuesday night. It was a goal that simply belonged on the training ground.
The Reds notch their fifth goal in the 54th minute as Firmino glances Coutinho's free-kick into the bottom corner.
Gerrard Houllier and Rafael Benitez were given big money to spend during their time as Liverpool managers, but Brendan Rodgers and now Klopp have been restricted for whatever reason by the structure now in place at the club.
Picking up the ball after a neat through-ball from Daniel Sturridge, Oxlade-Chamberlain burst through the Maribor defence with one touch before sliding the ball past the oncoming keeper. And right at the end, Trent Alexander-Arnold's shot from distance deflected in.