Last season's runners-up have endured a woeful first half to their domestic campaign and will start 2015 in the automatic relegation spots.
Dortmund suffered their 10th Bundesliga defeat of the season on Saturday as Klopp's men went down 2-1 at fellow strugglers Werder Bremen.
Klopp has previously guided Dortmund to two league titles as well as the DFB-Pokal in his time at Signal Iduna Park, while also reaching the UEFA Champions League final in 2013.
And Zorc explained that he, Klopp and chief executive Hans-Joachim Watzke had met following the reversal in Bremen and agreed they still had the right man for the job.
"Hans-Joachim Watzke, Jurgen Klopp and myself sat together [on Sunday] and discussed and analysed our situation," he told Kicker.
"We are convinced that we will manage to get out of this current difficult situation together."
Part of Dortmund's woes this season can be explained by a lengthy injury list, with the likes of Marco Reus, Henrikh Mkhitaryan, Mats Hummels and Ilkay Gundogan all missing for varying spells this term.
On the possibility of bringing in new players during January, Zorc explained: "I never rule anything out generally.
"We have concrete ideas of what we want to realise."
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