A patchy run of form - which saw Dortmund win just one of their last six Bundesliga matches before the mid-season break - means last year's UEFA Champions League finalists sit fourth in the German top flight.
An injury crisis, particularly to the club's defensive players, has not helped Klopp, with Bayern Munich, Bayer Leverkusen and Borussia Monchengladbach all ahead of them in the standings.
Finishing fourth would mean Dortmund would have to play in the 2014-15 Champions League's qualifying stages - and risking missing on the financial gains of Europe's premier club competition is not on the club's agenda.
Watzke told newspaper Suddeutsche Zeitung: "At the moment fourth place is acceptable, but we would not be satisfied with a fourth-place finish at Borussia Dortmund.
"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."
Dortmund host eighth-placed Augsburg in their next Bundesliga fixture on January 25.
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