Nagelsmann requested to be relieved of his duties on Thursday following Germany's early exit from the World Cup, and the DFB has granted that request, immediately terminating their contractual relationship with the 38-year-old former Bayern Munich boss.
"The DFB will now seek talks with Jurgen Klopp," the federation said in a statement.
"He has already signalled his general willingness to take on the position."
According to Bild, the DFB would like to present Klopp as the new Bundestrainer within the next five weeks, with officials hoping the vacant post is filled by early August at the latest.
Klopp would need to be bought out of his contract with Red Bull, which runs until 2029, before any appointment could be confirmed.
Germany's World Cup ended on Monday when the four-time champions were beaten by Paraguay on penalties in the last 32.
Nagelsmann initially appeared determined to stay in the role, saying after the defeat: "I'm not someone who runs away."
But in Friday's statement announcing his exit, he struck a different tone.
"I've done a lot of thinking in the days since our elimination and have consulted with trusted individuals both personally and within the federation," he said.
"The decision was anything but easy for me. My top priority has always been the team's success. After such a bitter disappointment, they deserve the chance for a fresh start."
It was Nagelsmann's second major tournament in charge, with Germany having reached the Euro 2024 quarter-finals as hosts before losing in extra time to eventual winners Spain.
Germany have not won a World Cup knockout match since they were crowned champions in 2014, having gone out at the group stage in 2018 and 2022 under Joachim Low and Hansi Flick respectively.
Nagelsmann, who also managed RB Leipzig and Hoffenheim in the Bundesliga, replaced Flick in September 2023 on a contract initially running to Euro 2024, before it was extended first to this year's World Cup and then to Euro 2028.
DFB sporting director Rudi Voller paid tribute to his outgoing coach.
"After the disappointing World Cup exit for everyone, Julian's decision deserves our respect, because he's taking responsibility where he'd like to continue shaping things, and putting the national team as a whole above himself," Voller said.
"Of course, we all would have liked a different outcome to the tournament and a more convincing performance from our team. But Julian is and remains an excellent coach, and I'm convinced he'll continue on his successful path."
Nagelsmann's departure is the first of several expected changes at the DFB following a third consecutive disappointing World Cup, with chief executive Andreas Rettig also set to step down at the end of the year.
The futures of sporting director Rudi Voller and DFB president Bernd Neuendorf are also reportedly under discussion.