Kaellenius, who will take over from Dieter Zetsche after the company's annual general meeting on May 22, has been working for months on a cost cut initiative, dubbed "Move", which is expected to be ready in the summer, the paper said.
Central administration costs are to be cut by about 20%, the paper said, adding billions of euros in efficiency potential would be targeted.
Daimler declined to comment.
Kaellenius said earlier this month that Daimler will cut development costs of new Mercedes-Benz cars by a significant amount by 2025 and will intensify alliances with rivals as a way to improve margins.
(Reporting by Christoph Steitz; editing by David Evans)