The four-time World Cup champions were sent packing after their penalty defeat to Paraguay in the round of 32 on Tuesday (June 30).
While Nagelsmann remains in the job for now, speculation is mounting that the young manager could be sacked by the DFB any day.
Former Liverpool manager Jurgen Klopp is reported to be ‘open’ to returning to the dugout for the Germany job, and Schweinsteiger is a big fan of the idea.
Speaking as a pundit for ARD, when asked about whether Nagelsmann will be sacked or not, Schweinsteiger responded: "I believe that it will happen.
"Of course, nothing is certain yet. But I have a feeling that it will likely happen that way."
Schweinsteiger then gave Klopp his backing: "If Jurgen Klopp were to become national coach, he would also bring such a power base with him.
"The DFB is already in a state of emergency, and I have the feeling that it will happen."
"After an exit like that, it is always the case that you have to talk about the coach," Schweinsteiger added.
"I believe that Jurgen Klopp is a great coach and that he can create a sense of new optimism. I think that would be very important with a view to the European Championship."