The coach has responded to rumours linking him with a move for the Manchester City striker
With Mario Gotze leaving the club for Bayern Munich in the summer, top goalscorer Robert Lewandowski has been strongly tipped to follow in his footsteps out of Signal Iduna Park.
And with reports linking Dortmund with a move for Manchester City striker Dzeko, Klopp responded to the speculation and admitted the former Wolfsburg man is on his radar.
"I do not know anything of a meeting with Dzeko," he had told Sky. "But if you think about what will happen to us in the next few years, we have to think about him.
"But judging by information we have, the wages he is content with technically do not fit ours, as we will not bend. We do not throw about peanuts.
"Still, we will leave all doors open."
Dortmund and Bayern Munich played out a dress rehearsal of their Champions League final on Saturday, with the two sides playing out a 1-1 draw.
Mario Gomez levelled for the visitors after Kevin Grosskreutz had put BVB in front and Klopp was happy with the efforts of his side, despite the game effectively being a dead rubber with the Bavarians already crowned champions.
"Nobody wanted to arouse suspicion that it was a friendly match," the 45-year-old acknowledged to reporters. "Had we played a little more, we could have caused more problems to the opponent.
"We had some rotation but started really well [with the opener], and then [Ilkay] Gundogan had to be taken off. We would have liked to win, but I'm happy of course."
Klopp was involved in an angry confrontation with FCB sporting director Matthias Sammer following the sending off of Bayern defender Rafinha, but the BVB boss simply added that "it just happens" when quizzed on the incident after the game.