Portugal's attorney-general, Fernando Jose Pinto Monteiro, has promised to announce a "solution" to a case that has gripped the world since Madeleine vanished on May 3 last year.
It is believed that police and prosecutors will be forced to admit they do not know what happened to the girl and must therefore shelve the inquiry.
More than 14 months after the child went missing, Mr and Mrs McCann, both 40, 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 this month for prosecutors to consider whether to bring charges, request further inquiries or close the case.
Mr Pinto Monteiro fuelled expectations of a major announcement tomorrow when he told reporters in Lisbon: "The 'Maddie Case' will have a solution on Monday and you will hear of it."
It is expected that the police files will be shelved, although they will be periodically reviewed and could be reopened if new evidence emerges.
Under Portuguese law, the authorities could still maintain the McCanns' arguido status - but reports have suggested this is unlikely.
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.