Dortmund won the Bundesliga in 2011 and 2012 and were runners up in 2013 and 2014.
Klopp's side dropped to 18th in the German table when Werder Bremen beat VfB Stuttgart 2-0 on Saturday, a result that lifted them off the bottom.
Now rock-bottom Dortmund face a home game with high-flying Borussia Mönchengladbach, who are third, on Sunday.
The last time that 2013 Champions League finalists Dortmund found themselves bottom of the Bundesliga was August 2007, while Klopp took charge in July 2008.
Dortmund's dire domestic form is sharply contrasted by their European campaign having already qualified for the last 16 in the Champions League with two games to spare after four consecutive wins.
Klopp is waiting on the fitness of his Germany stars, winger Marco Reus and goalkeeper Roman Weidenfeller, who are suffering from gastroenteritis, while Gladbach who are on a club record run of 17 games unbeaten, welcome back Germany squad member Max Kruse from injury.
Dortmund face Arsenal away and Anderlecht at home in their remaining Champions League Group D games and are five points clear of Arsene Wenger's Gunners.