The firm's management and supervisory board decided that the opposition of shareholder Asklepios made it impossible to run the company properly, the newspaper reported.
In April, Fresenius made its initial offer for Rhoen, but after Asklepios took a 5 percent stake in Rhoen, Fresenius failed to reach the 90 percent threshold it had set itself for the bid.
Rhoen's bylaws require approval of more than 90 percent of shareholders if it wants to change its equity capital or take other major strategic decisions.
Asklepios subsequently made it more difficult for Fresenius to reach those 90 percent by saying it planned to buy more than 10 percent in Rhoen Klinikum.
Sources had told Reuters in August, without revealing the value of a possible new bid, that Fresenius had been willing to settle for 50 percent of Rhoen plus one share, which at least would give it access to Rhoen's dividend.
But an unidentified source with knowledge of the matter told Die Welt that Fresenius then realized that a stable leadership of the company would not be possible with less than 90 percent ownership, leading it to drop its plans.
A spokesman for Fresenius declined to comment.
(Reporting by Peter Dinkloh and Axel Hildebrand; editing by G Crosse)
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