Montgomery Sibley, her former lawyer, has appealed to the United States supreme court for permission to publish the contents of the so-called “black book” - said to contain 15,000 pages of phone records.

Mr Sibley told the National Enquirer that “time is of the essence” in publishing because it has phone numbers containing information “relevant to voters before they cast their ballot”.

A lower court has already barred him from releasing the numbers or naming names.

Investigators have told the National Enquirer that the numbers referred to by Mr Sibley were probably those of Mr Cruz, reported RadarOnline website, which said it had seen a copy of the magazine’s forthcoming report, due to be published on Wednesday.

“If Montgomery Sibley has what he says he has, it has to be Cruz,” said Wayne Madsen, who belonged to a team of reporters who investigated Palfrey’s business for Hustler, a monthly pornographic magazine.

“Going on what I know about the other male candidates still in the race, it isn’t any of them, and Palfrey didn’t provide call boys, so it wasn’t Hillary.”

Dan Moldea, another investigator who examined three of the four boxes of contacts Mr Sibley gave him before the lawyer was subjected to a court gagging order, said he could not recall any other current candidates being on the list.