Wulff left office in February 2012 in disgrace when the investigation into his financial affairs was officially launched. At the time he said he was resigning because he had lost the faith of the public rather than for any wrongdoing - and is now going to fight for his reputation.
Hannover's public prosecutor offered to drop the corruption investigation in return for a payment of €20,000, but Wulff's lawyers confirmed on Tuesday they had rejected the idea.
The focus is a 2008 hotel stay by Wulff and his wife at a hotel in Munich, which was paid for by film producer David Groenewold - shortly before Wulff who was then state premier of Lower Saxony, asked Siemens for money to fund a Groenewold project.
The public prosecutor said on Tuesday: "The investigation is about to be concluded." But whether, and if so when, charges would be pressed against Wulff remained open.
Wulff's lawyers said the allegations against Wulff were unfounded and the entire process should be dropped. "We are fighting here for the reputation of the former Federal President," said Bernd Müssig, one of his lawyers.
It appears that several conditions attached to the prosecutor's offer had been unacceptable for Wulff - including the statement which would go with it that Wulff would accept criminal legal responsibility. Although Wulff would not have a record due to this, it could be interpreted as an admission of guilt, his lawyers said.
The prosecutor's office interviewed more than 100 witnesses, searched Wulff's private home and piles of documents.
The investigation was sparked by a report about a soft loan of €500,000 that Wulff got from a Lower Saxony businessman friend, with which he paid for the house. This led to a string of allegations of blurred lines between personal, business and political advantage and, after just two years in office, his resignation.