The German Football Federation (DFB) confirmed the move on Friday, adding it was seeking talks with Klopp, who it said had expressed interest in the position.
"Stakeholder representatives and the supervisory board of DFB ... on Friday unanimously decided, on the proposal of DFB president Bernd Neuendorf, to immediately terminate the contractual relationship with Germany coach Julian Nagelsmann," a statement said.
"Nagelsmann had already asked in a confidential conversation with the association's leadership the previous day to be released from his duties.
"The stakeholder representatives and supervisory board have now granted that request."
Nagelsmann's fate was sealed after the team lost 4-3 on penalties against outsiders Paraguay in the first knockout game on Monday, with most of the criticism directed at Nagelsmann.
Four-time champions Germany had also lost their last group match against Ecuador, after winning their first two games at the tournament against Curacao and Ivory Coast.
Former Hoffenheim, RB Leipzig and Bayern Munich coach Nagelsmann, 38, landed the national team job in September 2023, succeeding Hansi Flick.
Nagelsmann oversaw 37 matches, of which Germany won 23, with seven draws and seven defeats. He led the team to the quarter-finals of the home Euros in 2024 and into the Nations League finals last year.
Former Borussia Dortmund coach Klopp is now the official frontrunner to take over. The 59-year-old is currently head of Red Bull's global football operations.
"With regard to filling the coaching post, the DFB leadership will now seek talks with Jurgen Klopp," the DFB statement said.
"He has already signalled his fundamental willingness to take on the position."
Germany's next match is their Nations League start on September 24 against the Netherlands. Greece and Serbia are the other opponents in the group stage, which runs until November.
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