Der Spiegel magazine said the married couple had been working undercover in Germany. Known as Heidrun and Andreas A., both suspects deny the accusations.
Police reportedly walked in on the woman while she was listening to encoded radio transmissions. A task force from the German Federal Police or Bundeskriminalamt (BKA), arrested the pair last Tuesday in Marburg and Balingen, in central Germany.
They also confiscated two Austrian passports that appeared to have been forged.
The documents stated that Andreas A. was born in Argentina, while Heidrun A.'s birthplace was listed as Peru. But inquiries made by German authorities in South America confirmed that the passport data had been falsified.
Der Spiegel said authorities believe the two alleged spies have been working in Germany since the KGB, the Soviet Union's spy agency, was still in operation.
They started investigating the couple after the Federal Bureau of Investigation busted a Russian spy ring in the United States.