Klopp claims November's prize after guiding the leaders eight points clear at the top of the Premier League table with four victories from as many matches.
He is only the second manager in history to pick up the award in three of the first four months of a top-flight campaign, after Pep Guardiola in 2017/18.
"It feels really good," Klopp said. "But I don't take it personally. My players are responsible for that, obviously, because they have so far played an outstanding season."
After extending his contract at Anfield on Friday he told Liverpool's official website: "This club is in such a good place, I couldn't contemplate leaving.
"This is a statement of intent, one which is built on my knowledge of what we as a partnership have achieved so far and what is still there for us to achieve."
Liverpool's flawless November included a 3-1 success against Manchester City, while the Reds also beat Aston Villa, Crystal Palace and Brighton & Hove Albion, and Klopp is targeting a fourth Barclays award of the season with an impressive December.
Klopp said: "If I get it next month that would mean we have a pretty good December, which is a pretty busy one, so that is my target actually!"
Overall it is the sixth time the German has won the award, which was decided after votes from the public were combined with those of a panel of football experts.