The front page story caused a sensation around the world, as it was the first suggestion that detectives were treating the McCanns as suspects.
This week the couple, from Rothley, Leics, withdrew their defamation action after being advised that the newspaper had a strong defence under Portuguese law.
It could argue the story was published in good faith because senior police officers did at the time believe the McCanns may have been implicated in the case.
A source close to the couple confirmed that the defamation action against the newspaper and two journalists had been dropped.
The source said the McCanns want to concentrate instead on their £1 million case against Goncalo Amaral, the former head of the Madeleine investigation.
They also suspect Amaral may have been behind the story in Tal & Qual, which has since folded.
The source said: "The libel action against Tal & Qual has been dropped for a number of reasons. Firstly, the newspaper went bust some time ago.
"Secondly Tal & Qual could probably have mounted a defence, as they were reporting what a certain police officer believed at the time.
"Kate and Gerry have been advised it is much better to go for the source of the story.
"When the story first came out it was a huge shock for Kate and Gerry and they did not believe it was true."
The Tal & Qual article was published three months after Madeleine went missing during a family holiday in Praia da Luz, on the Algarve.
It claimed that detectives believed the parents had either caused a fatal accident or had given drugs to their daughter.
Lawyers representing the McCanns filed a writ against the newspaper, its editor Emidio Fernando, and reporter Catarina Vaz Guerreiro.
But two weeks later the couple, both doctors, were sensationally named as "arguidos" or formal suspects in the case.
Deluded chief investigator Goncalo Amaral wrongly believed they had covered up their three-year-old daughter´s death, even though there was no evidence to support his theory.
He was later taken off the case, which was eventually archived and remains unsolved.
In July 2008 the McCanns were cleared of any wrongdoing in a formal report by Portugal´s Attorney General Jose Pinto Monteiro.
They have always believed their daughter was abducted.
Mr Fernando said: "I had total faith in the source and was certain the police were looking at the couple.
"It's not a victory, because I never saw this as a war. I was, as I am today, totally calm about what I wrote."
Gerry and Kate McCann´s spokesman Clarence Mitchell said: "This is a matter for Kate and Gerry´s lawyers in consultation with Kate and Gerry, of course."
Amaral, 49, went on to make more than £1 million by writing a book repeating his outlandish claims.
The McCanns are suing him for at least £1 million for defamation and for breaching their human rights.
They have employed one of Portugal´s leading libel lawyers, Isabel Duarte, in a case expected to be heard in Lisbon next summer.
If they win they will use the money to continue the search for Madeleine, who would now be six.
The Find Madeleine Fund, set up to finance the couple's worldwide search for their daughter, is expected to run out of money by the end of the year, it was reported this week.
The McCanns also plan to sue the group behind a leaflet blaming them for Madeleine´s disappearance.
The couple were "deeply upset" by the fliers, produced by a group called the "Madeleine Foundation", which has accused them of neglect.
The leaflets were received by 10,000 people in the McCann's home village of Rothley.