"A major portion of this theft occurred while Mr. Apotheker was CEO of SAP," Ellison alleged in a statement issued by Oracle.
He said Oracle will offer evidence that Apotheker was involved when the trial starts next Monday in a federal court in Oakland, California.
HP did not immediately respond to requests for comment.
Oracle is seeking billions of dollars in damages in the case. It has accused SAP and its TomorrowNow subsidiary of stealing thousands of bits of software, including big fixes and patches, as well as other support material from Oracle in order to provide reduced-price maintenance service for Oracle customers.
SAP has admitted to illegal downloads from an Oracle website and the trial is expected to focus on how much the German software maker should pay Oracle in damages.
SAP has maintained that Apotheker and other top executives did not know about the illegal downloads initially and then moved to stop them once they discovered the problem. Oracle has maintained that SAP executives knew about the issue for years.