Emmanuel Faber, the chief executive and chairman of French food group Danone, told the weekly Journal du Dimanche that he did not hold a "dogmatic" view as to whether the role should be split in two.
Faber is facing calls from activist investor Bluebell Capital Partners to step down after it took a stake in the company late last year.
Danone shares fell 27% in 2020 and the company had been touted as a prime target for an activist fund.
"The separation of the roles of chairman and chief executive has been the object of multiple debates for years," Faber told the newspaper in an interview published on Sunday. "Is it indispensable? In any case, I do not hold a dogmatic view on the matter."
Faber has been chief executive since 2014 and also took on the chairman's role three years later.
He had intensified actions to try and ward off activist investors just as the COVID-19 pandemic further complicated the group's outlook and sapped its sales to the restaurant sector.
It announced a plan to cut 2,000 jobs in November and said it would trim product ranges. Faber confirmed the job cuts included 400 in France.
Faber said the pandemic had cost the group sales worth 1 billion euros. Sales of mineral water fell 30%, he said.