Her parents Kate and Gerry McCann are both official suspects in the case, along with a third man Robert Murat.
But two newspapers claim the police have said they “do not have sufficient evidence” to charge the McCanns.
Madeleine, from Rothley, Leics, was three when she disappeared from the resort of Praia da Luz on 3 May 2007.
The Correio da Manha newspaper said on Tuesday that sources within Portugal’s judicial police said they “do not have sufficient evidence to allow formal charges to be brought against the McCanns in the disappearance of their daughter”.
The Jornal de Noticias said: “The police have not found the guilty.”
The newspapers said the closure of the investigation would be announced within the next few days.
The McCanns’ spokesman Clarence Mitchell told the BBC the couple did not know yet whether the reports were correct.
“If they are true, it’s to be welcomed that Kate and Gerry are not to face any charges,” Mr Mitchell said.
“It’s quite right. They are innocent of any involvement in Madeleine’s disappearance. They have suffered enough in this process.”
Mr Mitchell said that if the investigation was to be closed, all the information held by the police must be made public so the McCanns could carry on their own search for Madeleine.
“What happens to all those leads, all those contacts? There are thousands of pieces of information in those files,” he said.
“What we don’t want them to do is lie on a shelf somewhere gathering dust.”
Mr and Mrs McCann are due to go to the High Court on 7 July to ask a judge to order police files on the disappearance of their daughter to be released.