According to a report in the Süddeutsche Zeitung (SZ), "influential circles" within the DFB are mulling making a criminal complaint to the police on suspicion of a breach of confidence.
The complaint would centre around a €6.7 million transfer from the DFB into a Swiss account belonging to world football's governing body, Fifa, in 2005. According to the DFB, the money was intended for a "culture programme" at the 2006 tournament.
Spiegel magazine reported last week that the money was re-transferred by Fifa into an account belonging to ex-Adidas boss Robert Louis-Dreyfus. The weekly magazine claims that Dreyfus had provided an identical amount of money to the DFB five years earlier to buy key votes among Fifa delegates to ensure that Germany was awarded the World Cup.
Zwanziger, who in 2005 was deputy leader of the DFB's steering committee for the World Cup, is alleged to have overseen the transfer of the €6.7 million to Fifa. The SZ reports that a long feud has raged between Zwanziger and the DFB, and that it appears the federation is seeking to place blame for the scandal upon him.
DFB members have previously said that the money was intended for an opening ceremony that was cancelled at the last minute.
But the Interior Ministry told the Munich daily that "on the basis of the documents at its disposal" that it has no evidence of a payment from the DFB to Fifa for an opening ceremony nor any indication "of a planned or actual sharing of the costs of the opening ceremony on the part of the DFB".
Should it transpire that there was no transparent reason for the money to be transferred, the DFB is reportedly considering demanding it back from Fifa.
German prosecutors said on Monday that though they were not yet formally investigating the allegations surrounding the 2006 World Cup, they were looking into the reports.