The six-time champions of Europe will be heavy favourites to continue that winning run in what is their first ever meeting with Midtjylland, who were beaten 4-0 at home by Atalanta BC on matchday one.
Here, Sports Mole looks at how Jurgen Klopp could set his side up for the contest.
Liverpool were boosted by the early return of Alisson Becker in goal against Sheffield United, but they will have to wait until at least the weekend to welcome other key men back.
Chief among those is Thiago Alcantara, who has missed the last two games with a knee injury and has also been ruled out of this game.
Virgil van Dijk and Alex Oxlade-Chamberlain are long-term absentees, while Kostas Tsimikas continues to recover from a thigh problem.
With Liverpool such firm favourites for this match Klopp may consider taking the opportunity to rest one of his attacking stars, and Sadio Mane could be first in line for that - particularly given the form of Diogo Jota, who scored on his first Premier League start at the weekend.
Jota's inclusion in that match saw Klopp switch to a 4-2-3-1 formation which is again an option here, although any rest of Mane would likely see a switch back to the more familiar 4-3-3.
It could be a landmark night for Mohamed Salah, who will make his 50th Champions League appearance if selected.
A hat-trick for the Egyptian would see him surpass Steven Gerrard as the club's leading goalscorer in the history of the competition, and he has directly contributed to nine goals in as many home group games for the Merseysiders.