Reports, quoting unnamed sources in Dubai, claimed that Deborah Parry, 38, who was born in Nottingham, had been given the death sentence for the murder of her Australian colleague Yvonne Gilford.
Associated Press claimed that Lucille McLauchlan, 31, from Dundee, had been cleared of murder but found guilty of being an accessory to murder.
The Foreign Office moved quickly to say that it had "no information" that any such decisions had been made.
Relatives of both Gilford and the British nurses also expressed bewilderment.
Frank Gilford, the brother of the dead nurse, who has suggested that he would seek the death penalty if the British nurses were found guilty, described the reported development as a "non-event".
He said: "I have still not heard anything from Saudi Arabia. I have no confirmation on any of the stories floating around the countryside."
The British families were clearly upset by the rumours.
Jack Irvine, a spokesman for the families, said: "It is clearly very, very distressing to the relatives.
"If you were the parent or relative of someone in a Saudi jail and they were possibly about to be beheaded wouldn't you be distressed?
"We have been getting this every weekend for the last three weeks. The same story. When it is checked out it appears to be untrue."
The Foreign Office said that, as far as it was aware, no decision had been made.
"Our situation is that we have also made inquiries and the senior officials to whom we spoke said that they had no information on a judgment being issued or a verdict and sentence handed out," said a spokesman.
Officials said they did not believe that information was being withheld from the British authorities.
"But their judiciary is independent of the government so we are not to know the ramifications any more than we would know [the private deliberations] of the higher courts in this country." He added: "We would expect that the first people to be told would be the lawyers on both sides."
It has been confirmed that papers from the case were submitted to a higher Saudi court 10 days ago. Sources have speculated that this indicates that a decision has been made and sent for approval.
But according to Salah al-Hejailan, the nurses' Saudi lawyer: "The documents of the case were submitted to a higher court in Riyadh last Saturday [August 23[...[and] did not give a judgement of any kind."
Mr Hejailan said the documents submitted dealt with issues such as the nurses' alleged confessions and the Gilford family's insistence on the death penalty, and the higher court would now review the evidence and determine the credibility of the confessions.
The Dubai-sourced reports claimed that a three-judge panel had issued its verdict on 17 August, but had not released it publicly. An appeals court in Riyadh is reviewing the case as part of a mandatory appeals process that could last months or even years, it was claimed.
Verdicts issued by Saudi courts are not always immediately released publicly and court hearings are closed to reporters.
The Australian nurse was found murdered in December in her room at the King Fahd medical complex in the Saudi city of Dhahran. She had been stabbed, bludgeoned and suffocated.
Ms Parry and Ms McLauchlan say they are innocent of the murder and have withdrawn their confessions which they say were made under duress.