He befriended the McCanns in the weeks after their daughter went missing, entertaining them at his house on two occasions and keeping in contact by phone and email.
The McCanns are said to be “horrified” by the discovery that Freud was a paedophile.
His family, who include the PR executive Matthew Freud, have said that Freud was not in Portugal at the time of Madeleine’s disappearance and that they have not been contacted by police.
However, officers from Operation Grange, the ongoing Metropolitan Police investigation into Madeleine’s disappearance, are expected to assess the new information before deciding if it may be relevant to the inquiry.
Freud was unmasked as a child sex abuser after one of his victims contacted ITV’s Exposure documentary team, who also broke the story of Jimmy Savile’s paedophilia four years ago.
Sylvia Woosley said Freud befriended her family in 1948, when he was working at a hotel in the South of France, and started abusing her when she was 10.
Four years later, following a family crisis, her mother asked Freud and his wife Jill if they would look after Mrs Woosley, and she found herself living under the same roof as her abuser, being brought up as a daughter. The abuse continued until she managed to move away when she was 19.
Another woman told ITV that Freud started abusing her in the 1970s, when she was 11, and eventually raped her when she was 18, by which time he was a Liberal MP sharing an office with Cyril Smith, who was also unmasked as a paedophile after his death. The rape was so brutal that his victim bled for a week.
Both women’s accounts have been passed on to the Metropolitan Police.
Lady Freud said: “This is a very sad day for me. I was married to Clement for 58 years and loved him dearly. I am shocked, deeply saddened and profoundly sorry for what has happened to these women. I sincerely hope they will now have some peace.”
Freud, who was knighted in 1987, was best known as a popular panellist on the Radio 4 show Just a Minute from 1967 until his death in 2009.
The grandson of the psychoanalyst Sigmund Freud and the brother of the painter Lucian Freud, he worked his way into the heart of British society, and when he died the then Prime Minister, Gordon Brown, was among the mourners at his funeral.
His five children include Matthew Freud and the broadcaster Emma Freud.
A spokesman for the McCann family said they had not until now been aware of Freud’s child abuse and were not aware that he had ever been investigated by Operation Grange.
The Metropolitan Police did not respond to questions about Operation Grange, but former murder squad detective Colin Sutton said: "If this is something that investigators had not been aware of then it would be certainly a potential line of inquiry that would be worth pursuing.
"It is not something that ought to be taken lightly and you would also want to look any connections he may have had in the area at the time."