Nagelsmann has paid the price for Die Mannschaft's World Cup disaster, his tenure ending just four days after Monday's penalty shoot-out defeat to Paraguay.
The result meant Germany, who had been eliminated at the group stage in both 2018 and 2022, again failed to reach the round of 16.
Nagelsmann had a contract running until Euro 2028, but chose to leave his position after effectively being told to fall on his sword or be sacked.
The DFB confirmed both Nagelsmann's departure and Klopp's interest in taking over in an official statement.
"Regarding the appointment of a new coach, the DFB leadership will now seek talks with Jurgen Klopp," the statement read. "He has already signalled his general willingness to take on the position," it continued.
Klopp, 59, has not coached since leaving Liverpool in May 2024.
Since then, the former Bayern Munich head coach's rival has worked as Red Bull's Head of Global Soccer, as well as taking up a role as a television pundit.
He was working at the World Cup for German broadcaster Magenta and did not hold back in dissecting the national team's problems on air.
On occasions, his assessments of Nagelsmann's Germany side were scathing.
Klopp's willingness to step in comes at a low point for German football, with the DFB now searching for a way to arrest back-to-back-to-back early World Cup exits.
Talks between Klopp and the federation are expected to move quickly given his stated interest and Germany's need for a swift appointment before the new international season.