
Kate and Gerry McCann are widely expected to be formally cleared by the Portuguese authorities of involvement in Madeleine's disappearance.
Portugal's attorney-general, Fernando Jose Pinto Monteiro, has promised to announce a "solution" to the case.
But it is believed that police and prosecutors will be forced to admit they cannot prove what happened to Madeleine and must therefore shelve the inquiry.
More than 14 months after the child went missing, Mr and Mrs McCann, both 40, from Rothley, Leicestershire, remain "arguidos", or formal suspects, in the case.
In recent weeks Portuguese newspapers, citing anonymous sources, have repeatedly reported that police have not found enough evidence to lay charges.
Detectives handed over their lengthy final report at the start of July for prosecutors to consider whether to bring charges, request further inquiries or close the case.
If the case is shelved, the McCanns want their own private investigators to be given access to detectives' papers so they can continue the search for their daughter.
British police have travelled to Portugal to meet the public prosecutor in the Madeleine case.
The Leicestershire Police officers held discussions about how evidence would be disclosed at the end of the investigation into the young girl's disappearance.
A Portuguese newspaper reported that the British officers tried to stop certain information - including results of a DNA test on a sample from the McCanns' hire car - from being made public.
The request was denied by public prosecutor Jose Cunha de Magalhaes e Meneses at a meeting in the Algarve town of Portimao, according to the newspaper.
A Leicestershire Police spokeswoman refused to comment on the report.
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