Sources close to the Bavaria-based brewer of organic, non-alcoholic drinks, said the majority shareholder, beverage company Rhön Sprudel, was keen to sell off its share.
The Sal. Oppenheim bank is rumoured to be involved in the deal, with German beer company Krombacher, Hövelmann, and Pepsi also showing interest in purchasing the company, the paper reported.
Bionade, which has sales of €70 million a year, is considered one of the pioneering firms in the manufacture of organic and healthy soft drinks.
Handelsblatt reported that the owner of the Bionade trademark, the Peter-Leipold family, is said to have signalled interest in a deal.
Coca-Cola previously made an offer for the Bionade trademark in 2004 but was rebuffed.
Neither the company itself nor the family wanted to comment on the deal. Also Coca-Cola was on Friday not available for a comment, the paper said.