Rummenigge admits he regrets the decision to hire Jurgen Klinnsmann as manager in 2008 - after the club held productive talks with Klopp.
The German giants were on the lookout for a new manager after Ottmar Hitzfeld quit the club to take charge of the Switzerland national team. Klopp was available after quitting Mainz, where he had built up a reputation as one of German football's most promising managers.
"Uli was in talks with Klopp at the time. We had to make a swift decision and then we agreed to get Jurgen (Klinnsmann)," Rummenigge told ZDF Sport.
Rummenigge admits he regrets the decision to hire the German icon.
He added: "I was partly responsible for bringing Jurgen Klinsmann on as a coach. Unfortunately, that didn't work.
“That was also due to FC Bayern, but it just didn't work. I'm very sorry. It wasn't a good decision for both parties."