Non-executive Chairman Norbert Winkeljohann is looking into internal and external candidates with the goal of presenting a designated successor by the next annual shareholder meeting in April 2023, it cited people familiar with the matter as saying.
Baumann, who engineered Bayer's troubled takeover of Monsanto, in 2020 was given a new contract until 2024.
He said at the time he could have been given a longer term but opted for a shorter contract to accommodate his personal plans.
Bayer declined to comment.
The company's stock has been battered by billions of euros in writedowns and litigation costs, in large part related to the $63 billion Monsanto takeover.
But the operating outlook for its agriculture unit, the world's largest maker of seeds and pesticides, has improved this year as demand from farmers is being bolstered by rising food prices.
(Reporting by Ludwig Burger; Editing by Kirsten Donovan)