Media speculation about Madeleine has been rife in Portugal
Last week, Tal & Qual reported that the "police believe" Kate and Gerry McCann killed her, with the paper suggesting Madeleine may have died in an accident.
The McCanns' lawyers will file for defamation, saying the "untrue" story had caused "suffering and humiliation".
Police have stressed that the McCanns, of Rothley, Leics, are not suspects.
Four-year-old Madeleine vanished from a holiday apartment in Praia da Luz, Algarve, on 3 May while her parents were eating at a nearby restaurant.
Earlier this month the police said there were indications that Madeleine might have died.
The newspaper's front-page story, headlined "The police believe the parents killed Maddie", claimed the couple had either caused a fatal accident or given drugs to their daughter.
The allegations were attributed to a "source close to the investigation".
However, the director of police has said publicly that the McCanns have never been viewed as suspects.
Lawyers for the couple will file a seven-page defamation complaint against the journalist who wrote the article and the newspaper's director. The legal case says the story was completely untrue.
Media speculation has been rife in Portugal since the police declared that Madeleine might have died.
The BBC's Steve Kingstone, who is in Praia da Luz, said the McCanns had previously held back from responding to the speculation, but now felt "a line had been crossed" and "enough was enough".
The newspaper's claim was based on the discovery of suspected traces of blood inside the family's apartment.
The UK's Forensic Science Service is continuing to analyse evidence recovered from the apartment.
Last week, Mr McCann asked the media to end the constant speculation about his daughter's whereabouts.He said there had been "huge amounts written with no substance" and that it was not necessary to "bombard people on a daily basis" with Madeleine's image.