Speaking at a press conference to unveil a 44-man split squad for upcoming Nations League matches, Klopp said Germans should feel able to express pride in their country without being associated with extremism.
"I don't want to leave national pride to the wrong people," said Klopp, one of the country's most prominent public figures.
Without mentioning the AfD by name, he added that he would like to "reclaim the flag."
"I want it so that when someone waves it, no one thinks: 'What is wrong with you?'," said Klopp.
"Instead, I want people to understand: You are happy and realise how lucky you were to be born, grow up, or move to this wonderful country," he said.
The AfD trounced mainstream parties to win an election in the eastern state of Saxony-Anhalt on September 6th, and could form the first far-right government at state level in postwar Germany there. It could also top the polls in another state election this weekend.
"There have been an incredible number of things happening recently: an election took place which some people probably thought was fine, whilst many others thought, 'Good heavens, what on earth is going on?'," Klopp said.
An AfD spokesperson said the party would issue a statement later on Thursday.
'Positive patriotism'
German Finance Minister and Vice Chancellor Lars Klingbeil said he shared Klopp's view, saying the German flag - with its three horizontal stripes in black, red and gold - was not a symbol of exclusion or arrogance.
"People can be proud of this country, regardless of whether they were born here, have immigrated here, or their family has lived here for generations," he told Reuters.
"National pride and an open-minded attitude towards the world are not mutually exclusive."
Wearing a cap with an Adidas logo in the colours of the German flag, Klopp acknowledged the sensitivity of patriotism in a country that has long viewed overt displays of national pride through the prism of its Nazi past.
The former Liverpool manager, who begins his Germany tenure against the Netherlands on September 24th, said he preferred the term "positive patriotism" to "national pride", which he feared could be misunderstood.
"Can you be proud to be German and still be open, diverse, nice and friendly - can you still show compassion?" Klopp said.
"I am 100 per cent certain: Yes!"
The secretary general of Chancellor Friedrich Merz's Christian Democrats, Franziska Hoppermann, welcomed Klopp's call to not leave Germany's symbols to the extremists.
"We all should, and are allowed to, wear our national colours with pride and confidence as symbols of our freedom," she told Reuters.