The latest initiative aims to determine when co-Chief Executive Anshu Jain first learned of possible attempts to manipulate benchmark rates such as Libor at Deutsche Bank and in the industry in general, the magazine reported.
Investigators recently discovered that critical electronic records were destroyed in early 2012, including telephone conversations that took place around the time that Lehman Bros. collapsed in 2008, the magazine said.
German regulator Bafin, which has hired auditors Ernst & Young to pursue new lines of query, declined to comment.
Deutsche Bank said it was cooperating with regulators and conducting its own probe into possible manipulation of Libor (the London interbank offered rate), a benchmark against which around $450 trillion of financial products from derivatives to home loans are priced worldwide.
"As per current status of investigations, we can say that no current or former member of the management board had any inappropriate involvement," a spokesman said in an emailed statement.
Investigations into the possible abuse of reference rates such as Libor or foreign exchange fixings have dogged banks since a post-crisis regulatory backlash struck the financial sector.
Deutsche Bank has paid at least 5.6 billion euros ($7.5 billion) in the past two years in fines and settlements and expects to pay around 3 billion euros more this year.
Bafin's queries extend beyond the core, seven-member management board and target managers including the bank's 20-member executive committee, Der Spiegel said.
Bafin said in May it hoped to conclude its Libor investigations in the summer. Bafin and other euro zone supervisors will hand over responsibility for overseeing the area's biggest banks in November to the European Central Bank.
(Reporting by Thomas Atkins; editing by Jane Baird)