Stadler's arrest on Monday threw Volkswagen (VW) into turmoil as it struggles to recover from cheating revelations, which emerged after regulators blew the whistle in September 2015 on the carmaker's use of illegal software.

The directors of Audi and Volkswagen discussed how to run its more profitable division without Stadler, but failed to come to a conclusion, the carmaker said late on Monday.

"The supervisory boards of VW and Audi have not yet reached a decision and continue to assess the situation," a spokesman for VW said.

The arrest has kicked off a new debate over VW's governance which could raise tensions on its supervisory board, putting at risk a fragile truce between management, VW's controlling Piech and Porsche families, as well as representatives from labour and the region of Lower Saxony.

VW has for years said only lower-level managers knew of the emissions cheating, but US authorities filed criminal charges against former VW boss Martin Winterkorn earlier this year, and Munich prosecutors widened their probe into Audi this month.

Munich prosecutors said Stadler was being investigated for suspected fraud and false advertising and for his alleged role in helping to bring cars equipped with illegal software on to the European market.

Following his arrest, Munich prosecutors said Stadler, the most senior active VW official to be remanded in custody since the scandal broke, was being held on fears he might hinder their investigation.

On Monday, VW and Audi directors were discussing the leadership crisis in separate meetings, with one source saying Dutchman Bram Schot was the front runner to become interim Audi chief.

Germany's Sueddeutsche Zeitung newspaper said VW's supervisory board had already picked Schot for the job and only needed the formal approval of Audi's directors. VW denied any such appointment had been made.

Australian Associated Press