Madeleine McCann disappeared from her bed when on holiday with her British family in Portugal in 2007.
McCann's disappearance, from her bedroom in a rented holiday home in the Algarve, sparked one of Europe's biggest international investigations
On Friday, the prosecutor general's office in Portugal said there were no records of crimes committed by the suspect in the Algarve.
"We assume that the girl is dead," Braunschweig state prosecutor Wolters said. "The public prosecutor's office in Braunschweig is investigating a 43-year-old German national on suspicion of murder."