Ecclestone, 83, went on trial in Munich in April over allegations he bribed a former German banker as part of the sale of a major stake in the motor sport business eight years ago.
If convicted, the British billionaire could face up to 10 years in jail and would have to cede control of a business he has built up over the past four decades.
“Public prosecutors and the defence are discussing the possibility of an agreement,” a spokesman for the German authorities said.
Media reports said Ecclestone, who denies wrongdoing, on Tuesday offered to pay German state-owned bank BayernLB 25 million euros ($33.5 million) to help settle the case. There was no immediate comment from his defence team.
Prosecutors have rejected a request from the defence to drop proceedings on the grounds of a lack of evidence.
Under German law, a settlement payment to a party involved would not necessarily bring a criminal case to an end.
The court said in a statement that talks on an agreement could continue, but it also scheduled a further hearing in the case for next Tuesday.
Ecclestone is required to attend every session, but hearings are held only a couple of times a week to fit in with his globe-trotting schedule as chief executive of the motor racing business.
Ecclestone is accused of channelling $44 million to jailed BayernLB banker Gerhard Gribkowsky to smooth the sale of a major stake in the business by the bank to private equity fund CVC, which became the largest shareholder in Formula One in 2006.
The prosecution alleges that Ecclestone wanted CVC to take control because this meant he could stay on as chief executive of a business he had been instrumental in building.
Gribkowsky had been chief risk officer at state-owned bank BayernLB, which became a major shareholder in Formula One following the collapse of the Kirch media group in 2002.
Ecclestone says he paid off Gribkowsky as an “insurance policy” after the German threatened to make damaging false claims about his tax affairs. He funded the payment with a commission taken from BayernLB after the sale to CVC.
Under German law, judges, prosecutors and the defence can agree to dismiss a case or settle it with a light punishment, although terms for such an agreement are strictly defined.
Ecclestone has previously offered to pay money back to BayernLB in 2012 to try to prevent the case from going ahead but that proposal was rejected. ($1 = 0.7456 Euros)
(Writing by Keith Weir; Editing by Mark Heinrich and Jane Baird)