The Liverpool manager, who picked up the award last year, pipped Bayern Munich manager Hansi Flick to the 2020 prize on the merit of votes cast by national team bosses, with Bielsa finishing third.
Klopp was surprised to hear his name announced, having expected Flick to win for his title treble. Under his care Bayern won the Champions League, Bundesliga and DFB-Pokal.
"I don't know why people voted for me but for me Flick deserved it for his titles," said Klopp, whose Liverpool side won the Premier League title last season.
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Bielsa led Leeds back into the Premier League, winning the Championship by 10 points and ending the Whites' 16 year exile from the top flight.
Klopp put on record his admiration for the Argentine.
"He's doing an incredible job at Leeds," he said.
"[Not winning this award] doesn't say anything bad about Marcelo Bielsa, one of the most influential coaches in world football. I have never met anyone who had anything bad to say about him.
"He is known as a great football brain, winning an award or not does not make you a bad coach. My opinion doesn't change about him, he's an incredible, incredible coach."