A source close to the McCanns slammed the petition, telling the Sun: "Kate and Gerry will not do a lie detector test because they've got nothing to lie about.
"It's just nonsense to suggest they have."
Three-year-old Madeleine disappeared from Portuguese resort Praia da Luz in May 2007 as her parents were dining at a nearby tapas bar.
Kate, 49, and Gerry, 48, are bracing themselves for the painful milestone 10th anniversary of their daughter's disappearance in just five weeks.
The couple, from Rothley, Leicestershire, are clinging on to a glimmer of hope that the girl, who would now be aged 13, nearly 14, could still be alive.
Maddie's parents were recently hit with a fresh blow of anguish after a long civil battle.
Last month, the Portuguese Supreme Court ruled they had not proved they were innocent in the disappearance.
The McCanns accused the Supreme Court judges who ruled against them in their court fight with ex-police chief Goncalo Amaral of nonsensical "contradictions".
Furious Gerry and Kate made it clear through lawyers that they strongly disagreed with the judges' "erroneous" premise the lifting of their status as "arguidos" or formal suspects did not mean they were innocent of any involvement in their daughter's May 3, 2007 disappearance.
Portugal's Supreme Court issued its devastating put-down in February when it backed Amaral over his hurtful 2008 book The Truth of the Lie, in which he claimed the McCanns faked Madeleine's abduction to cover up her death in their Algarve holiday apartment.
Earlier in March, Portuguese crime expert Moita Flores made the outrageous claim Madeleine died in an apartment in the resort.
The hunt for Madeline, which has cost more than £12 million ($21 millon), could be in its last year as topped-up funds are set to run out at the end of March.
