Porsche's management delivered the claim in written form to counterparts at Audi, the newspaper said without citing its source.
Audi admitted in November 2015 that its 3.0 liter V6 diesel engines used in about 80,000 VW, Audi and Porsche models were fitted with an auxiliary device deemed illegal in the United States.
The German government earlier this year ordered a recall of Porsche's Cayenne sport-utility vehicle (SUV) and prohibited registrations of the model's diesel version, and said as late as June of this year that it had detected new cheating. And Porsche's former R&D chief was recently arrested in the scandal.
Porsche wants compensation from Audi for the costs of the retrofits, legal counseling and customer measures, Bild said.
A spokesman for Porsche said VW group-internal issues were not meant for public discussion, without elaborating. Audi declined comment and referred inquiries to Porsche.