Christian Brueckner lived in Portugal's Algarve region at the time McCann vanished, and is due to be released from prison in Germany later in September. He was first named as a suspect by British and German police in 2020.
"We have requested an interview with this German suspect but ... it was subsequently refused by the suspect," Detective Chief Inspector Mark Cranwell from Britain's Metropolitan Police said in a statement.
McCann went missing on May 3, 2007, while on holiday with her family in the Algarve town of Praia da Luz, sparking a frenzied search and gaining the attention of the world's media. She has never been found.
Brueckner remains a suspect in the Metropolitan Police's own investigation, the police statement said, adding the force was aware of the pending release from prison of the 49-year-old.
The convicted child abuser and drug dealer is behind bars for raping a 72-year-old woman in the same area of the Algarve.
Officers will continue to pursue any viable lines of inquiry, the British police statement added.
Portuguese and German police spent four days in June searching for evidence related to McCann's disappearance in the Algarve.
"We can provide no further information while the investigation is ongoing. Any questions about the conditions around his release should be directed to the German authorities," the statement added.
German police said in June 2020 that McCann was assumed dead and Brueckner was likely responsible. Brueckner has denied any involvement and has not been charged with any crime related to the case.
