The company is working with Credit Suisse on the sale with firms such as Cinven, EQT Partners AB and Triton Advisors possibly lining up bids.
Bayer also wants to float its plastics unit on the stock market, according to the story that broke first on Bloomberg, and use the proceeds of both deals to invest in life-sciences businesses.
It agreed in May to buy Merck & Co’s over-the-counter drug business for $14.2bn. Bayer chief executive Marijn Dekkers is also interested in acquisitions in veterinary medicines.
The firm is reportedly interested in the $22bn animal health company Zoetis, which separated from Pfizer.
Shares in Zoetis rose 1.6 per cent yesterday, closing at a record $44.58. Bayer’s shares climbed 1.2 per cent to $147.42.
Last month, Bayer raised its revenue and profit forecasts.
The diabetes unit makes products such as the blood-glucose meter Contour, which had annual sales of more than €700m (£5.6m) in 2013.