According to the Friday edition of the Danish publication Weekendavisen, the 49 year-old Finn, who works at the University of Copenhagen, is accused of helping Russian spies in Denmark.
The professor confirmed to Yle that on the 28th of last month he was charged with aiding or attempting to aid a foreign espionage organisation. Kivimäki was first arrested in 2010. In his message to Yle, he said that he had been questioned by Danish security services for 350-400 hours.
The newspaper Jyllands-Posten reports that officials in Denmark have confirmed one arrest, but have declined further comment.
The Finnish professor says that he had conversations with four Russian diplomats that Danish security services claim are spies, but Danish officials have provided no evidence to back up the claim. According to Weekendsavisen, he says that for a fee he provided professional analysis and scientific thinking about security policy to the Russians, as he has done for a number of other diplomats and governments.
In his letter to Yle, Kivimäki claims that the Danish intelligence services tried to obtain information about the Aceh peace process from him in 2005.
Another Finnish professor at Copenhagen University told Yle that the information could relate to natural resources in the Arctic, an area in which both Denmark and Russia have interests.
Kivimäki is being charged under section 108 of the Danish criminal code. Under this section of the law, a person can be charged for assisting spies of a foreign power on Danish soil, even if he or she has not personally engaged in espionage. The maximum penalty if convicted is six years imprisonment.
No one has ever been brought to trial under this law. A former head of the Danish intelligence agency told Yle that the charges only require that the professor knew he was dealing with a foreign intelligence agency, the information he handed over does not need to be secret or classified.
He added that Kivimäki is suspected of giving information about his students, which the foreign agency might then use to recruit agents in Denmark. The State prosecutor is to decide on 26 April whether the trial should be held behind closed doors. The trial itself is to begin on 8 May.
The University of Copenhagen has declined to comment on the matter. The professor has been suspended from his job. Danish television says that he is highly respected in his field.