Porsche chief Wendelin Wiedeking could be offered a 100 million euro (£86m) pay-off to quit and make way for a merger with Volkswagen, according to a German newspaper.
Sueddeutsche Zeitung claimed Wiedeking had been visited by Porsche chairman Wolfgang Porsche, who "made it clear" that he should step down.
Wiedeking has been criticised for his role in allowing Porsche’s holding company to amass debts of more than nine billion euros (£7.8bn) during its failed attempt to take over VW.
He also opposes a plan by Ferdinand Piech, VW chairman and a part-owner of Porsche, to merge Porsche and VW.
But when he arrived at Audi's centenary celebrations, Wiedeking insisted that he would be staying in his position.
“I am a happy CEO and feel fit and well in the role,” he said.