The 46-year-old replaced Bert van Marwijk at the struggling Bundesliga side on Monday, and will be hoping to put an end to their eight-game losing run in all competitions.
Hamburg have plummeted down the league table since November and last weekend's 4-2 defeat to bottom club Eintracht Braunschweig sealed Van Marwijk's fate.
They are now one point off the bottom of the table and face a fight to avoid a first-ever relegation from the top flight.
Conversely, Dortmund arrive at the Imtech Arena full of confidence after four successive league wins, in which they have scored 12 goals while only conceding two.
Jurgen Klopp's side have only lost twice on their travels in the league this season and scored five in their last away Bundesliga match at Werder Bremen earlier this month.
Dortmund suffered an uncharacteristic slump in form before the mid-season break, but they have not lost since the league resumed and are slowly closing in on second-placed Bayer Leverkusen.
A 4-0 victory against Eintracht Frankfurt last time out, combined with Leverkusen's 2-1 defeat to Schalke, saw Dortmund move to within a point and rekindle hopes of finishing runners-up behind leaders Bayern Munich.
Hamburg's recent record against Dortmund will give Slomka a glimmer of hope - they have won two of their last three meetings but were convincingly beaten 6-2 at Signal Iduna Park earlier this season, with Pierre-Emerick Aubameyang and Robert Lewandowski each netting twice.
The hosts will be without captain Rafael van der Vaart after he was ruled out with a torn ankle ligament, so the pressure will be on top scorer Pierre-Michel Lasogga to fire them to victory.
Dortmund's injury list is slowly lightening with Mats Hummels and Marco Reus both returning to training on Wednesday, leaving only Neven Subotic and Jakub Blaszczykowski (both knee) out.
