The Bosnian international is one of a handful of centre-forwards that have been linked with the German champions as a replacement for Robert Lewandowski, who has been tipped to leave in the summer.
However, Klopp has admitted that any new arrival would have to fit into the club's current wage structure.
"[Dzeko] is an extraordinary forward," Klopp told Sports Image. "Falcao for example is great as well. One thing we can say about these names, but also about others: At Borussia Dortmund, everything was made regarding our conditions and salary structures. We won't cancel this for any player in the world.
"That is what he has to do by himself. If and when Robert Lewandowski leaves, a new forward has to accept our conditions. Then he is interesting.
"If anybody wants to come to us, he has to adapt financially. Then he can have real fun, probably more than at his old club."
Dzeko joined City in January 2011 from German side Wolfsburg.