Christian B is currently in prison in Kiel, Germany for drug offences.
He was given a seven-year sentence for raping a 72-year-old woman, which he will begin serving in January 2021.
The key suspect in the Madeleine McCann case attacked the American woman in 2005, in Portugal’s Praia da Luz – the same area where three-year-old Madeleine disappeared in 2007.
Police revealed that Christian B was main suspect in the case in June, as part of a new appeal for information about the girl’s disappearance.
He has previously been convicted for sexually abusing children.
The rejection of his appeal means Christian B, as he is known under German privacy laws, will remain in jail beyond January, when his term for the drug offences ends.
He was extradited from Italy to Germany on drug trafficking charges in 2018, before being separately convicted of rape and handed a seven years prison sentence.
The 43-year-old man has not been convicted of any crime related to Madeleine McCann’s disappearance.
Christian B challenged the validity of the extradition on the grounds that it cited a drugs conviction but not a rape charge.
Police have said he was frequently living in the Algarve region, where Madeleine was last seen, between 1995 and 2007. They said he had worked in the area as well as committing crimes including burgling hotels and dealing drugs.
Portuguese police reportedly believe the German investigation into the man has wasted precious time as they ruled him out as a suspect shortly after the four-year-old girl went missing from a resort in Praia da Luz.
German prosecutor Hans Christian Wolters said he believes Christian B was responsible for Madeleine’s disappearance and that while prosecutors have evidence leading them to believe he killed her, it is not strong enough to charge him with.
The case is still a “missing persons” investigation in the UK because there is no “definitive evidence” to show whether Madeleine is alive or not, the Metropolitan Police said in July.
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