Two Portuguese newspapers said the Public Prosecutor's office intended to call off their search for the girl before July 14, when the customary official secrecy period covering the investigation ends.
Police could reopen the case if new evidence emerges, the papers said.
The papers - Correio da Manha and Jornal de Noticias - cited unidentified police sources.
Madeleine disappeared on May 3, 2007, days before her fourth birthday, after she was left sleeping in a holiday apartment as her parents Kate and Gerry dined with friends in a nearby tapas bar in the resort of Praia da Luz in southern Portugal.
Her parents were made formal suspects on September 7 last year in one of the many dramatic twists in the case. They insist Madeleine was abducted.
Clarence Mitchell, the McCanns' spokesman, told Sky News: "As usual, these are non-attributed sources and we have not heard this officially. But if it is true it's not before time - Kate and Gerry have suffered enough.
"Police should lift their arguido (suspect) status and should pass their information over to our investigators who continue to work on the case.
"We still need to find Madeleine."
Sky's Crime correspondent Martin Brunt said: "If the police stop treating the McCanns as suspects the couple would hope that more effort would be put into finding their little girl."
Another Briton, Robert Murat, was also declared a suspect in the case.
Portuguese journalist Rui Pinto de Almeida told Sky News: "This is a formal legal requirement in Portugal and there remains the possibility of reopening the case."
The Expresso newspaper says on its website that, according to a police source, the report on the investigation has not reached any conclusions and does not say whether it is a case of abduction, homicide, or concealing of a body.
Another source told the newspaper: "In normal circumstances, with this sort ofa report, the decision would have to be to shelve it in the hope of getting better evidence in the future."
The final report is to go the Ministerio Publico in Portimao, where a decision will be taken in the coming days, according to the newspaper.
- Where does this investigation go from here?
- Yet Again the whole world learns of a development in this case 'BEFORE' her parents!
- Will the arguido status be lifted from Kate and Gerry?
- There have been questions asked of Kate and Gerry, but it is worth noting, that there has not been one witness report that places Mr Mrs McCann anywhere they should not be.
- In contrast there has been upwards of 12 eye witnesses that place the other suspect 'Robert Murat', where he says he wasn't.
- There are many questions that need to be asked of Robert Murat and it will be interesting to see if these questions have been asked, when the McCann's get to see their file, which apparently, may happen around mid August! Not least Robert Murat apparently has had three alibis as to his whereabouts that evening.
- 'Coincidentally' Goncalo Amaral, who was sacked from this investigation in September 2007, retired yesterday 30th June 2008 and today this news is leaked to the Portuguese press!
- Chief Inspector Paulo Rebelo took over this investigation when Goncalo Amaral was sacked, yet NOT ONCE, has this man contacted the parents to keep them informed about what is being done to investigate their daughter's disappearance!
- Even if Mr Rebelo chooses to abide by the Portuguese secrecy laws in this one instance, it is still incredible that the man in charge of this investigation has never once spoken to Kate and Gerry in their position as arguidos (suspects) and he has chief investigating officer.
- How could he possible mount a search for Madeleine, or investigate her disappearance if he hasn't bothered to talk to two out of the 3 suspects?
- Does this point to the fact that there was 'NEVER' any evidence to charge these parents and never any reason for Rebelo to speak to them, so their arguido status was always a farce right from the word go!
- There have been many question marks that have come to light over the alibi of Robert Murat, not least many eye witnesses that actually place him where he says he wasn't, yet apparently (unconfirmed) Rebelo has only spoken to this an once!
- Of course Portugal has a different way of investigating and policing, but the level of incompetence and bungling in this investigation has been absolutely appalling.
- There is a whole litany of errors, leaks, smears and briefings against Kate and Gerry McCann to the Portuguese press, which are said to have come from the now infamous 'a source close to the PJ said.........'
- The sad truth of this investigation is that it is absolutely no further on that the very first minute of little Madeleine's disappearance and this is an appalling indictment on modern day policing, in ANY country.