Klopp agreed an early termination of his contract with the Bundesliga club on Wednesday and will leave the club at the end of the season after seven years in charge.
A haul of two Bundesliga titles, a DFB-Pokal crown and a run to the UEFA Champions League final makes the task of replacing Klopp a somewhat daunting one.
However, Watzke said they hope to confirm their new boss in the next week and cooled speculation that former Mainz boss Thomas Tuchel was a shoo-in to take up the role.
"I do not know who the new coach will be and even if I did, I would not say it," he told reporters.
"A second division manager it will probably not be. I would also caution against thinking too one-dimensionally in the direction of Thomas Tuchel.
"We will not wait around forever for a solution. I think that we will arrive at a proper and reasonable solution next week."
Dortmund have endured a difficult campaign this term and look set to miss out on the UEFA Champions League - something Watzke feels cannot be a regular occurrence.
"If Dortmund do not play internationally then we must then just go to the vault," he added.
"But in the medium term we must return to the Champions League. It is crazy that in the latest [financial] tables Leicester City received €50 million more than Bayern Munich.
"Maybe it helps us continue to stay creative when it comes to player development. At this rate, England will never be world champions."
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