Business monthly Manager Magazin cited unidentified sources as saying the supervisory board had asked for time to consider the request from Eckhard Cordes, who was passed over for job of replacing outgoing Chief Executive Juergen Schrempp.
Chrysler division head Dieter Zetsche will get the top job when Schrempp steps down at year's end, the board decided.
DaimlerChrysler was not immediately available to comment on the report.
A separate newspaper report said DaimlerChrysler Chairman Hilmar Kopper was also set to resign. DaimlerChrysler would not comment.