Bild, citing its own information without elaborating, said Nagelsmann decided to resign after a three-hour "secret summit" on Thursday at the German Football Association (DFB) headquarters in Frankfurt.
The DFB did not immediately respond to an emailed request for comment on Friday.
The paper said Nagelsmann had been urged to consider a voluntary departure after presenting his explanation for Germany's round-of-32 exit to Paraguay on penalties earlier this week, and that he would receive an estimated €7 million ($8 million) payoff.
Germany's defeat by Paraguay in Boston on Monday marked a third successive World Cup flop after first-round exits in 2018 and 2022. They won the World Cup for a fourth time in 2014.
Nagelsmann, appointed in 2023 and the youngest coach in a World Cup knockout game in four decades, had said after the loss that he was "not someone to say 'I'm stepping down' just because we were eliminated".