Kate McCann, 39, was named an official suspect in order to be asked 22 detailed questions by Portuguese police, the family spokeswoman, Justine McGuinness, told reporters.
"They have suggested that blood has been found in a car that they hired 25 days after Madeleine was taken," McGuinness said. "Anyone who knows Kate would say to make an allegation of this kind about her is just completely ludicrous."
McCann was questioned for 11 hours Thursday and returned to the police station in Portimao the next morning for further questioning. Gerry McCann, who, like his wife, is a doctor, was also to be questioned, and the couple continued to strenuously profess their innocence Friday.
Gerry McCann's sister, Philomena, told ITV news that Kate McCann has been offered a plea deal of two years or less in jail if she admits to accidentally poisoning the child, ABC News is reporting.
"They tried to get her to confess to having accidentally killed Madeleine by offering her a deal through her lawyer – 'if you say you killed Madeleine by accident and then hid her and disposed of the body, then we can guarantee you a two-year jail sentence or even less,' " the sister said.
The British family was on vacation when Madeleine, who would have turned 4 on May 12, went missing.
The focus on the parents came after forensic tests revealed traces of Madeleine's blood in a car they rented 25 days after Madeleine's disappearance in Praia da Luz, Portugal, on May 3.
McGuinness said "there is a fear" that Kate McCann might be arrested.
"They believe they have evidence to show that in some way she's involved in the death of her daughter, which of course is completely ludicrous," McGuinness told reporters. "Kate is a lovely mother to her children. She'd never hurt them."
Gerry McCann is also expected to be named a suspect, family friend Clarence Mitchell tells the Associated Press.