Kelvin MacKenzie, former editor of The Sun, claimed in the paper today that one of the allegations involves Sir Cliff being on rollerskates when he allegedly abused a boy.
However, he did say that the allegations were highly improbable and he did not think Sir Cliff would be charged.
There has been widespread criticism of how the claims against the singer have been handled by South Yorkshire Police.
The force was slammed for tipping off the BBC before the star's house was searched in 2014, while he was on holiday in Portugal.
A report commissioned by a former police and crime commissioner found that the move "certainly interfered with his privacy and may well have caused unnecessary distress".
The 75-year-old has been voluntarily interviewed by police, but has never been arrested or charged.
Last year, the star's representatives attacked the Home Affairs Select Committee for publishing a letter from former Chief Constable David Crompton that revealed the police investigation had increased "significantly" in size and involved more than one allegation.
Sir Cliff's lawyers claimed the disclosure caused him a "further round of unnecessary and extremely damaging media coverage".
Earlier this year, DJ Paul Gambaccini, who has been cleared of historical allegations of sexual abuse following a lengthy investigation, has lent his support to Sir Cliff.
He said: "This case is a disaster for Great Britain. Sir Cliff is one of the greatest Englishmen of the 20th Century. This is a historic scandal."
This week, broadcaster Gloria Hunniford, a close friend of Sir Cliff, said he is facing an "unbearable strain" and has "become consumed" by the claims against him.
She said: "The toll on him has been enormous. It has to be with that kind of pressure of knowing you haven't done anything wrong but being accused."
South Yorkshire Police declined to comment on today's claims.
Earlier this week, a spokesman for Sir Cliff said: "It would be inappropriate to comment while the matter is under review."