The first former German president ever to face criminal charges, Wulff is suspected to have had an inappropriately cosy friendship with film producer David Groenewold.
Groenewold, who was charged on Friday for bribery, has admitted picking up the tab for Wulff and his then wife to stay at a luxury hotel in Munich in 2008 while Wulff was state premier of Lower Saxony.
In a statement released on Friday morning, state prosecutors said there was sufficient evidence to suggest the film producer's generosity had prompted Wulff to ask Siemens to contribute money towards one of Groenewold's film projects.
On Tuesday Wulff and Groenewold rejected the state prosecutor's offer of paying a fine, choosing instead to fight for their reputations in a possible trial. Wulff's lawyers said the allegations against him 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 on Tuesday.
Now it will be up to the regional court in Hannover whether to admit the charges and order a trial - a decision which could take months.
Wulff stood down in February 2012 amid a volley of allegations that he had blurred lines between personal, business and political advantage.