The 45-year-old coach, who has led the club to back-to-back Bundesliga titles, feels that its great rival lacks the same sense of togetherness Borussia Dortmund has.
Die Schwarzgelben defeated their rivals 1-0 in what was effectively a title-decider at Signal Iduna Park in April, before completing a league and cup double with a resounding 5-2 demolition Die Roten a month later.
Some Bayern players suggested after the latter loss that they had actually been the better side, and Klopp proclaimed his agreement, though with his tongue very much in his cheek.
"Of course Bayern was better! But we we scored the goals," he said during a speech to students on Wednesday. "And by the way, we have also beaten them five times in a row."
Then, when asked about the key to Dortmund's success, Klopp could not resist taking a another dig at Bayern.
"The family within the club comes above everything else," he explained. "This is important so that everything fits together. This often determines victory or defeat. This concept is practised differently in southern Germany..."
Klopp, who has won four trophies in as many years in charge, also made a point of revealing why he had elected to wear a Dortmund top to the talk.
"I chose this jumper, but I'm sweating like I pig. I want to show that I have maximum identification with the club."
Dortmund have lost Shinji Kagawa to Manchester United, but has been bolstered by the arrivals of Marco Reus, Leonardo Bittencourt, Julian Schieber and Oliver Kirch. Competition for places will therefore be particularly intense this season, with Klopp admitting that nobody is guaranteed a regular starting berth.
"In a team with our ambitions, to have a good chance, we must have always have 11 players in top form on the pitch," he mused.
"Everyone will get their games. Names do not decide themselves. I hope that we improve and people give us more credit."
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