Klopp's men finished runners-up to Bayern Munich in both the Bundesliga and UEFA Champions League last term but a spate of injuries has had an alarming impact on their progress this season.
With five first-team regulars sidelined, Dortmund have slipped to fourth in the German top flight and narrowly sneaked their way into the Champions League knockout stages in a dramatic final group game.
On the domestic front, Dortmund are winless in their last three outings, losing two and drawing one, and Watzke is keeping a close eye on their progess.
"At the moment fourth place is acceptable, but we would not be satisfied with a fourth place finish at Borussia Dortmund," he told Suddeutsche Zeitung magazine. "That is not our objective.
"We want to qualify directly for the Champions League, ideally, as this is not out of our reach and of course I expect us to play better in the second half of the season."
Any hope of wrestling the Bundesliga title from Pep Guardiola's Bayern Munich has seemingly evaporated, with the leaders already 12 points clear of Dortmund at the top of the table.
Dortmund get their Bundesliga campaign back under way on January 25 when Augsburg visit the Westfalenstadion.