The McCanns have described new reports about a man Portuguese police allegedly suspect kidnapped Madeleine as "pure speculation".
The 40-year-old had been fired from the Ocean Club holiday complex in Praia de Luz where the McCanns were staying when their daughter disappeared on May 3, 2007, and may have been seeking revenge, Portuguese daily Correio da Manha said.
He died in a tractor accident in 2009 but police have interviewed his widow as part of their new investigation, according to the newspaper.
Clarence Mitchell, who represents Kate and Gerry McCann, said: "We are aware of reports in the Portuguese press.
"They are pure speculation and the McCanns are not going to give a running commentary on every new report."
It is claimed that suspicions surrounding the former Ocean Club employee arose during a review by a judicial police team in Porto and led Portuguese authorities to reopen the case last week.
The man is reported to have been living in Lagos, just 15 minutes away from the holiday complex, at the time of the then three-year-old's disappearance.
Correio da Manha claimed that he had left the Ocean Club on bad terms and said that his possible motives for snatching Madeleine are under investigation.
It also reported that he was not on the list of employees given to police during the initial investigation because he was not working at the resort when the toddler disappeared.
Earlier this week, the newspaper reported that Portuguese investigators believe Madeleine is probably dead and are searching for her body.
Portuguese police have declined to comment on any of the claims due to a secrecy order relating to the investigation.
The latest reports come while a libel trial bought by the McCanns against a former Portuguese police officer who accused them of covering up their daughter's death is still ongoing.
Scotland Yard has issued fresh appeals to the public in recent weeks, releasing two e-fit images of a man who was seen carrying a child towards the beach the night Madeleine went missing.