Niersbach, who has been critical of both FIFA's handling of an ethics report on corruption for the awarding of the 2018 and 2022 World Cup as well as picking Qatar for 2022, said Germany should keep its voice in the powerful decision-making body.
"I run for this post because I want to support European positions and I am convinced that German football should not lose its voice in the biggest decision making bodies", Niersbach said in a DFB statement.
German football officials, including Niersbach and German league (DFL) chief Reinhard Rauball, have been vocal critics of FIFA's decision to award the 2022 tournament to the tiny Gulf state.
Desert temperatures make it far from ideal for the world's top soccer tournament while labour conditions of immigrant workers are also an issue, they said.
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Rauball, who has gone as far as saying the crisis within FIFA could lead to thoughts about UEFA breaking away from FIFA, said on Friday that Niersbach was the right man for the job.
"He can be the one to fight here for transparency and clearing up," Rauball said. "He has outstanding international contacts and enjoys the full backing of German football."
The 63-year-old Niersbach, who became DFB chief in 2012, recently proposed moving the 2022 tournament to the winter of 2023 so as not to clash with the winter Olympics and have cooler temperatures.
"With all due respect for the country which was awarded the tournament in a democratic way as long as there is no fact for the opposite, this world Cup bid should never have been accepted," Niersbach had said.
"UEFA doesn't think about staging the Euro on Cyprus. The World Cup dimension is just too big for Qatar and I have not even started talking about the heat or the intolerable conditions for migrant workers."
Zwanziger, Niersbach's predecessor at the helm of the DFB, is stepping down next year with UEFA, European soccer's governing body, electing its representative for the FIFA executive committee in March.
(Editing by Ed Osmond)
