The Manchester City striker has previously revealed he will one day return to Bundesliga, but the German champions' manager insists he will not be arriving at Westfalenstadion
The Bosnia international revealed in February that he "would love" a return to Germany after a successful four-year spell with Wolfsburg between 2007 and 2011.
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But Dortmund general manager Hans-Joachim Watzke similarly rejected claims in the press on Tuesday.
"This is total nonsense and not funny any more," he told sports news agency SID.
Dzeko scored 85 goals during his time in Bundesliga, and has admitted that infrequent appearances for the Premier League champions could force him to look elsewhere for regular first-team football - despite being City’s top goalscorer this season with 13 goals in all competitions.
And Klopp, regardless of a large financial windfall from Dortmund’s run in the Champions League this term, insists a move for the striker, who cost City £27 million two years ago, would be infeasible for his club.
Klopp, who previously described Dzeko as "extraordinary", added at a press conference on Thursday: "Dzeko is a good player but he is sadly out of our possibilities."
Dortmund’s current first-choice striker, Robert Lewandowski, has long been linked with a move away from Westfalenstadion – with Manchester United reportedly long-term admirers.