The hosts, meanwhile, are looking to cement their position in the Europa League qualifying positions in the table.
Both sides played more pragmatically than they have for most of the season, with Hoffenheim still having lingering fears of being relegated.
Wolf, of course, is fully aware that he was brought into the role to help shore up an increasingly leaky defence, and has moved to a back five system perhaps as a result of that.
Hoffenheim did not muster a single shot on target across the 90 minutes, which will have pleased Wolf from a defensive standpoint.
However, they may need to take the game more to a Koln side who will likely sit in and scrap for their lives given their current standing in the table, with more expected offensively from a side chasing a Europa League spot, but crucially without compromising their improved ability to defend transitions.
Indeed, Koln are staring relegation in the face after suffering a 3-2 loss at home to relegation rivals Mainz 05 last time out.
Markus Gisdol's side headed into the match knowing that a win would see them leapfrog their opponents and outside of the bottom three, but fell behind to an early strike from range by Jean-Paul Boetius, with the midfielder's effort crashing off the underside of the bar and over the line for his first goal of the season.
Ondrej Duda maintained his 100% record from the penalty spot to level proceedings before half time after Philipp Mwene was adjudged to have handled the ball, with Ellyes Skhiri turning the match on its head moments after the hour mark by nodding home at the back post from Jonas Hector's devilishly outswinging free kick.
However, Boetius turned provider with an excellent ball across Koln's box for Karim Onisiwo to equalise, before Leandro Barreiro's superb first-time finish snatched a dramatic winner for the visitors in injury time.
The defeat leaves Koln three points from safety with six matches remaining, with an inferior goal difference to 15th-placed Hertha Berlin meaning that even a win at Leverkusen on Saturday would not see them escape the bottom three.
Patrik Schick will be hoping for a start having only come off the substitutes' bench in Wolf's two matches so far, with the interim manager potentially looking to increase his side's attacking impetus.
Koln, meanwhile, will be without the suspended Duda after the forward picked up his fifth caution of the season in the defeat to Mainz, while Kingsley Ehizibue is ruled out after sustaining a head injury last time out.
Jan Thielmann will hope to recover from a muscle injury in time to feature from the bench.
Bayer Leverkusen possible starting lineup:
Hradecky; Jedvaj, Bender, Tapsoba; Diaby, Aranguiz, Demirbay, Wendell; Wirtz; Schick, Alario
FC Koln possible starting lineup:
Horn; Bornauw, Mere, Czichos; Jakobs, Skhiri, Hector, Katterbach; Wolf, Rexhbecaj; Andersson
We say: Bayer Leverkusen 1-1 FC Koln
While Leverkusen are aiming to qualify for Europe, there is clearly more at stake for the visitors, who desperately need to at least avoid defeat.
We can see them doing so, but it is unlikely to be the three points they require to keep within touching distance of their relegation rivals.
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