Klopp recently stated that he would love to coach the Sweden international at some stage of his career and the 31-year-old was quick to remind the BVB boss of his comments when the duo met during Monday's FIFA Ballon d'Or Gala at the Kongresshaus in Zurich.
"When are you bringing me to Dortmund?" Ibrahimovic asked Klopp in front of the television cameras.
"I would have to sell the whole team first," replied Klopp, only for the PSG striker to stress that he would happily make some sacrifices to join Dortmund.
"No, I will come to Dortmund for free."
"You are coming for free?" asked Klopp before turning to the cameras to have Ibrahimovic's comments confirmed: "Did you hear that?"
The 32-year-old attacker repeated his promise and joked that he hoped PSG president Nasser Al-Khelaifi wasn't watching the interview.
"I will come for free to Dortmund. This conversation is not for the PSG president."
Dortmund is in the market for a new striker following the transfer of Robert Lewandowski to Bayern next summer, but Ibrahimovic is unlikely to make the move to the Westfalenstadion.
The former AC Milan man has a contract with les Parisiens until June 2016.