VW, Europe's largest automaker, admitted in September it had manipulated the engines of around 11 million diesel cars, including its VW, Audi, Porsche, Skoda and Seat brands.
Engineers at Audi developed software capable of turning off certain engine functions in 1999, but it was never used by the VW luxury division, the newspaper said in an advance release of an article due to be published on Wednesday, which cited industry and company sources.
Six years later, when VW engineers at the firm's Wolfsburg headquarters were unable to bring nitrogen oxide emissions below legal thresholds, they started to install the software developed by Audi, Handelsblattsaid.
VW and Audi both declined to comment on the report, citing ongoing investigations by U.S. law firm Jones Day into the diesel emissions scandal. VW has said Jones Day will publish a "substantial report" on its findings by the end of April.
VW's supervisory board is due to discuss the potential costs of the emissions scandal and approve 2015 earnings on April 22, a day after a deadline for VW and U.S. regulators to agree a solution for U.S. cars fitted with the software. Reuters