The pre-tournament favourites suffered a shock defeat to Lyon on matchday one and sit bottom of the Group F standings, one point adrift of their opponents following the German side's away draw at Shakhtar Donetsk.
Excitement levels may be building ahead of Hoffenheim's inaugural home match in the Champions League proper, but the mood in the dressing room does not exactly match it.
Die Kraichgauer have failed to push on from last season's best-ever finish of third in the Bundesliga, finding themselves in a lowly 12th place after six rounds of matches.
Hoffenheim have lost three, won two and drawn one so far in the German top flight, leaving them four points adrift of the top four. To make matters worse for Julian Nagelsmann, his side's most recent loss came against his future employers RB Leipzig.
Nagelsmann will swap Hoffenheim for Leipzig next summer, but before then he will be desperate to leave his mark on the club he is soon to depart. The highly-rated German is already the competition's youngest ever manager, having presided over the 2-2 draw with Shakhtar at the age of 31 years and 58 days.
That point at the Oblasny Sportkomplex can be considered a positive return for the Champions League rookies, but there was also a tinge of disappointment as Die Kraichgauer twice led in Metalist through goals from Florian Grillitsch and Havard Nordtveit.
The 12th German club to compete in this competition, Hoffenheim were handed a direct route into the group phase, ensuring that they dodged the hurdle of the qualifying playoffs.
That is the stage they fell 14 months ago with defeat to eventual finalists Liverpool - their only previous experience of English opposition on the continent.
Hoffenheim instead had to settle for a place in the Europa League, and things did not exactly go to plan for Nagelsmann, as his side collected just five points and finished bottom of a group that also contained Braga, Ludogorets Razgrad and Istanbul Basaksehir.
Combined with the 2-2 draw at Shakhtar, the Bundesliga outfit now have just one win to their name in nine European outings, although they do remain without defeat in five after losing the first four of those matches.
Recent form in Champions League: D
Recent form (all competitions): WLDDWL
Man City finished well clear at the top of the Premier League last season, racking up a record number of points in the process, while also adding the EFL Cup to their growing collection of silverware.
The Citizens are top of the division after seven games of the 2018-19 campaign, too, as they look to become the first English side to retain the top-flight crown in a decade, and yet it could be argued that they have yet to hit top stride this term.
Pep Guardiola criticised his players for their failure to take more of their chances in a recent routine 3-0 win over Fulham, and the Catalan coach - a two-time winner of this competition - had further reason to be upset when watching his side succumb to a 2-1 loss at home to Lyon in their opening European fixture a few days later.
First-half strikes from Maxwell Cornet and Nabil Fekir gave Les Gones a two-goal advantage and, while Bernardo Silva did pull one back with a little over 20 minutes to go, City could not find a leveller to make it four successive defeats on the continent.
Never before had an English side lost four in a row in the Champions League, but that Lyon result, combined with defeat at home to Basel and back-to-back losses at the hands of Liverpool in last season's quarter-finals, means that Guardiola's men are in desperate need of a pick-me-up.
There is certainly a sense that Man City have unfinished business in Europe in what is their eighth consecutive appearance in the group stage, with their run to the semi-finals under Manuel Pellegrini in 2015-16 still their best-ever finish.
The Citizens may have cruised through the group phase last time out, thanks in part to wins away at Feyenoord and Napoli, but it is now just one win in six European ties - the other five ending in defeat for Guardiola's men.
Guardiola may argue that the Premier League is a better barometer of how successful his Man City tenure has been, but another failure to compete for the world's most famous club trophy this term will undoubtedly leave a blemish on his record.
Recent form in Champions League: L
Recent form (all competitions): WWLWWW
Guardiola revealed at the weekend that Sergio Aguero is still not 100% fit due to a foot injury picked up in the win at Newcastle United last month, leaving him doubtful for this midweek trip to Germany.
With a huge match against fellow unbeaten Premier League side Liverpool to come next weekend, it may well be that Gabriel Jesus is given the nod to give Aguero a breather, although changes are otherwise expected to be kept to a minimum.
Injuries to Benjamin Mendy and Fabian Delph will mean the versatile Oleksandr Zinchenko slotting in at left-back once again, and Danilo is an option on the right if Guardiola feels the need to leave out Kyle Walker.
In terms of the home side, Nagelsmann has a number of injury issues to contend with. As many as eight players could be missing on Tuesday evening, including defensive trio Kevin Vogt, Ermin Bicakcic and Nordtveit.
Kerem Demirbay returned from an adductor injury layoff in the defeat to Leipzig at the weekend, but he will likely be made to settle for another cameo role from the bench.
Hoffenheim possible starting lineup:
Baumann; Schulz; Posch, Vogt, Akpoguma, Kaderabek; Kramaric, Grillitsch, Bittencourt; Szalai, Joelinton
Manchester City possible starting lineup:
Ederson; Zinchenko, Laporte, Kompany, Danilo; D.Silva, Fernandinho, Bernardo; Sane, Jesus, Mahrez
Head To Head
Hoffenheim's 6-3 qualifying playoff defeat to Liverpool for last season's Champions League marked their first meeting against English opposition in any competitive European competition.
The Citizens have more experience of facing German sides and have won on two of their last four trips to the country - losing only one of those games, in contrast to five defeats in their first six visits.
That solitary loss came in a group-stage tie at Bayern Munich, but they have since played out a 1-1 draw with Borussia Monchengladbach two years ago.
We say: Hoffenheim 0-2 Manchester City
Hoffenheim, without back-to-back wins in all competitions since winning three in a row in April, head into this game sitting one point and one place above their opponents. Man City are strong favourites for a reason, however, and this fixture presents the perfect opportunity for the English champions to get their European campaign back on track.