The Reds won 2-1 in the first-leg in Germany thanks to goals from Trent Alexander-Arnold and James Milner, though Mark Uth's late handed Hoffenheim some hope for the return tie on Wednesday night.
The Bundesliga side are looking to embark on their first ever European campaign after a fourth-placed finish last term but must score at least two away goals to give themselves a chance of doing so.
Liverpool are looking to reach the groups for only second time in eight years and for the first time under manager Jürgen Klopp after themselves finishing fourth - in the Premier League - last term.
After a low-key start to their new campaign and having endured a turbulent summer transfer window, reaching the next stage would be a monumental uplift for Liverpool.
Their superior European pedigree, in addition to their first-leg advantage, makes them overwhelming favourites to reach the lucrative competition proper and in the context of their entire season, qualification is a necessity.
Looking to once again establish themselves as a consistent force on the continent, Liverpool must ensure last season's arduous domestic efforts are not in vain before even qualifying.
Klopp will ensure his charges do not underestimate Hoffenheim, despite achieving a feat that even Bayern Munich couldn't by becoming the first side since May 2016 to beat Die Kraichgauer on home soil last week.
Julian Nagelsmann's side are fully capable of overturning the deficit, having proved themselves a tactically-unpredictable energetic attacking outfit under their 30-year-old German manager.
They had chances at the Rhein-Neckar-Arena to travel to Merseyside on level terms, Simon Mignolet saving a penalty and making several fine saves while Benjamin Hübner powered a late header over, and will undoubtedly have their chances again on L4.
Liverpool were arguably fortunate to come away with a lead given Hoffenheim's opportunities and though the south-west German side need to score a minimum of two goals to progress, Liverpool's questionable defending will give them hope.
The Reds are likely to see more than the 37 per-cent possession they had in the first-leg, and will hope the infamous Anfield atmosphere on a European night can play its part, but will look to pose more of the same counter-attacking threat they showed in the first-leg.
They consistently broke with pace and precision when they bypassed Hoffenheim's counter-press and themselves could have scored more goals in the first meeting.
For that and many other reasons, the second-leg is all set up to be a hugely-entertaining contest and both teams will have to make better use of their chances if they are to secure themselves a place in Thursday's group stage draw.
Klopp could name a similar line-up to the first-leg after making five changes in their win over Crystal Palace on Saturday, benching the likes of Alexander-Arnold, Mohamed Salah and Emre Can.
Liverpool remain without want-away playmaker Philippe Coutinho, who is now sidelined by illness after a back injury, and Nathaniel Clyne and Adam Lallana - sidelined by hamstring and thigh injuries.
Daniel Sturridge is likely to drop back to the bench after starting, and lasting an hour, against Palace having recovered from a minor thigh injury.
Hoffenheim boss Nagelsmann rested several key players himself in their win over Werder Bremen at the weekend, though forward Ádám Szalai made his return from a calf issue.
The visitors' only absence is midfielder Florian Grillitsch, struggling with a metatarsal issue.
Recent form (all competitions):
Liverpool 1-0 Crystal Palace (S. Mané 73') - Premier League
Hoffenheim 1-0 Werder Bremen (A. Kramarić 84') - Bundesliga
Away goal permutations
Scoreline Hoffenheim need to progress:
Liverpool 0-2 Hoffenheim, 0-3, 0-4, 0-5 etc.
Liverpool 1-3 Hoffenheim, 2-4, 3-5 etc.
Liverpool 2-3 Hoffenheim, 3-4, 4-5 etc. - level on aggregate, Hoffenheim progress after scoring more away goals
Liverpool 1-4 Hoffenheim, 2-5, 1-5 etc.
Scoreline that forces extra-time:
Liverpool 1-2 Hoffenheim (3-3 on aggregate, two away goals each)
ANY other scoreline sees Liverpool progress
Liverpool are unbeaten in their last seven meetings in European football with German clubs. Their overall record against German teams reads: W18, D13, L6.
Liverpool have never lost at Anfield against a German team in Europe, winning 11 of 14 ties. Only FC Köln and Bayern Munich avoided defeat.
Ex-Borussia Dortmund and Mainz boss Jürgen Klopp has faced Hoffenheim 17 times as a manager, winning six, drawing six and losing five.
Liverpool are unbeaten in their last nine European fixtures at Anfield, winning six - including all of the last five - since defeat to Real Madrid in October 2014.