German large circulation newspaper Bild was first to report on the talks, with Porsche releasing a statement shortly after that.
Porsche declined to give any further comment to Reuters.
Both managers have been criticised for the company's poor performance and weak share price, the newspaper said.
In October, the carmaker said it would cut costs as it is struggling with a weakening economy and growing competition in China, the world's largest automotive market, and a slower-than-expected electric vehicle transition.
Porsche's shares, having initially performed strongly following their debut in September 2022, and even outperforming its parent Volkswagen (VOWG_p.DE) by market capitalisation, closed on the last trading day on Friday 30% lower than the IPO price.
