Klopp announced on Wednesday that he would leave the club in the summer following a disastrous campaign that sees BVB sat in 10th place in the Bundesliga.
His departure will bring to an end a seven-year spell in charge of the team, with former Mainz coach Thomas Tuchel being installed as the early favourite to replace him.
That said, Watzke maintains that he is not yet certain who will be handed the reins and says it is important to consider more than one candidate.
"I don't know who will be the new coach and if I did I would not say it," Watzke told Osthessen. "It probably won't be a second division manager but he will likely be German, but I would caution against thinking too one-dimensional in the direction of Thomas Tuchel.
"I think that we will have a proper and reasonable solution next week."
The club chief also insisted that Klopp's departure does not mean Dortmund will now endure a transitional period and expects them to move forward and enjoy more success.
"Borussia Dortmund is bigger than any individual. It goes on and on, the philosophy of Borussia Dortmund does not depend on the coach."
Klopp won two Bundesliga titles and reached the Champions League final in 2013 and remains in the race for the DFB-Pokal this season, with Bayern Munich awaiting in the semi-finals.