Reithofer is disappointed with costs at the company's Mini brand and for the BMW 1-series compact car, Manager Magazin said.
In a statement on Wednesday, BMW said in order to remain competitive amid rising costs, the company would seek to lower annual expenses "by several hundred million euros a year," but that is a far cry from the $5.4B rumored.
The cost savings are aimed at maintaining BMW's high profitability despite the company's growing investments in new drivetrain technologies, production expansion in markets such as the United States, Latin America and China, and increasing vehicle sales to new records.
BMW aims to boost worldwide vehicle sales to 2.5 million by 2016 from nearly 2 million last year. The company faces strong challenges from Audi and Mercedes-Benz, which both target BMW's position as the top-selling global premium automaker.
Reithofer wants to keep BMW's profit margin between 8 percent and 10 percent, the report said. Last year the company's automotive operations had a return on sales of 9.4 percent.
Last month, Munich newspaper the Muenchner Merkur said BMW intends to cut 100 million euros ($136 million) of German labor costs annually from 2015 onwards.