According to the newspaper, which did not identify its sources, Berlin would also buy a 7.5 stake in EADS from German banks and regional governments, giving Germany an equivalent stake to that held by France.
The transactions would cost the state €2.7 billion ($3.6 billion), the FTD said.
Although Daimler now owns 15 percent of the shares in EADS, it controls 22.5 percent of the voting rights, whereas on the French side, the state and the Lagardere group also control 22.5 percent.
Spain owns 5.5 percent of the aerospace group, which is the parent company of the aircraft manufacturer Airbus and the Eurocopter consortium.
On Wednesday Daimler said it wanted to find "a balanced solution" for France and Germany with respect to EADS, while Daimler chairman Dieter Zetsch added that "the shareholder structure will have to be discussed in the future."
Daimler has already reduced its holding twice and is believed interested in putting even more distance between itself and EADS.
Judges in France are pursuing Daimler in connection with an insider trading scandal centred on the European defence group following the sale by Daimler of a 7.5 percent stake in EADS in April 2006.
Two months later Airbus announced a major delay to deliveries of its A380 passenger jet, which sent EADS share prices plunging.