The two premium carmakers already have a joint procurement programme and recently extended their alliance to include development of advanced driver assistance systems and mobility services.
The talks over whether to cooperate on vehicle platforms could still fall apart, Sueddeutsche and Auto Bild said, without citing sources.
Both companies have acknowledged cooperation talks which include sharing engineering costs for driverless cars, but BMW and Daimler have repeatedly declined to comment on whether their cooperation could include entire vehicle platforms.
BMW's finance chief said in November he was open to deeper collaboration with Daimler but said it was difficult to identify win-win opportunities in the area of shared vehicle platforms.
Auto Bild said Daimler and BMW are in talks over whether to share engineering costs for compact and midsized cars, which are designed to be "electric first," but also have the capability of accommodating conventional powertrains.
BMW and Daimler would save 7 billion euros each, over a period of seven years, Auto Bild said.
Sueddeutsche Zeitung said the companies are seeking more than 7 billion euros in potential savings, and that if larger vehicles were included in the project, savings could be higher.
BMW and Daimler declined to comment.
(Reporting by Edward Taylor; Editing by Alexandra Hudson)