Katrin Lompscher, Berlin's Senator for Urban Development, plans to apply the cap to flats built until 2013, the report said, adding flats built from 2014 would be exempted.
The draft is still subject to discussions and could still change, the report said.
The Senate will prepare a bill to be sent to the city's parliament by Oct. 15. It is intended to take effect in January.
Berlin's city government in June decided to freeze rents for five years, heeding complaints from residents that their once famously affordable city was pricing them out.
Deutsche Wohnen is Berlin's biggest landlord with more than 115,000 flats in the German capital while peer Vonovia owns more than 42,000.
(Reporting by Christoph Steitz; Editing by Sandra Maler)