Gerry and Kate McCann pleaded for a convicted sex offender to "see sense" and co-operate fully with investigators searching for their missing daughter.
Raymond Hewlett, 64, has served several jail sentences for sexually assaulting young girls and is also wanted for questioning by British detectives for at least one unresolved sexual offence.
Mr Hewlett, a former soldier, was allegedly staying with his family at a campsite close to Praia da Luz in Portugal, where Madeleine McCann went missing in May 2007.
Police officers yesterday interviewed Alan and Cindy Thompson at a hotel in Canary Wharf, London, over their claim that Mr Hewlett was staying in a converted motor home with his German wife and their six children only an hour from the McCanns. Mr Hewlett allegedly told the couple he had been approached by "Gypsy travellers" offering to buy his daughter – just before Madeleine went missing on 3 May 2007.
He also talked about a business trip to Morocco, where there were several alleged sightings of the little girl in the first year after she disappeared, according to Mr and Mrs Thompson, who were holidaying in the Algarve at the time. The couple claim he told them he was 30 miles away in the market town of Fuesta when Madeleine vanished but it is unclear whether Portuguese police were ever aware of him.
There were unconfirmed reports yesterday that Mr and Mrs Thompson tried unsuccessfully to contact British detectives about their concerns about Mr Hewlett in the past.
The former Scots Guard, who is seriously ill in a German hospital after undergoing an operation for throat cancer, is under no obligation to speak to the McCanns' detectives but the couple hope he will agree to be interviewed within the next few days.
Clarence Mitchell, the McCanns' spokesman, said: "Mr Hewlett has denied any involvement in Madeleine's abduction. Our investigators hope he will see sense and co-operate by giving them whatever information is needed so they can eliminate him from the investigation. It's clear the man is ill and it's clear he has information that our investigators need. It is also clear that our investigators will be speaking to him in the near future."
Meanwhile, West Yorkshire police yesterday confirmed that they are awaiting permission from German authorities to interview Mr Hewlett over an unsolved indecent assault in 1975. He was first convicted of abducting and sexually assaulting a neighbour's 12-year-old daughter in 1972.
He is also under investigation by German authorities after his son, David, died falling from the back of a van that Mr Hewlett was driving from Portugal to Germany. Another son, Wayne Hewlett, has spoken out against his father in recent days, branding him a "monster" and "despicable".
Leicestershire police, which handle the British end of the McCann inquiry, refused to comment but said they would pass on any new information to Portuguese police, who remained in charge of the investigation.