The Dogan news agency said the shoe boxes were discovered on bookshelves in the home of Halk Bank's CEO, Suleyman Aslan, who is among dozens of people, including the sons of government ministers, detained for questioning as part of the corruption and bribery investigation.
Dogan, a reliable news source, cited unidentified judicial officials for its report. A national police official said he could not immediately confirm the report, while officials at the Interior Ministry refused comment.
Erdogan has suggested the probe is a politically motivated "dirty trap" to harm his government. The investigation comes ahead of local elections in March that are largely seen as a vote of confidence in Erdogan's 11-year tenure. He is expected to be a candidate in the presidential election in August.
The state-run Anadolu Agency said more than 50 people are in police custody as part of the investigation. Other reports said as many as 84 people were detained.