A privacy dispute involving a "well-known public figure", his former hairdresser and tabloid newspaper bosses is set to be analysed by senior judges.
Two judges have ruled that News Group Newspapers - publishers of The Sun - should not be barred from revealing the identities of people involved, following employment tribunal hearings.
But the "well-known" figure is preparing to ask appeal judges to consider the case and an injunction barring publication of names remains pending a Court of Appeal hearing.
Detail of the case emerged earlier this month in a ruling following the latest in a number of employment tribunal hearings.
Mrs Justice Simler refused to overturn a decision by a less senior judge who had concluded there no reason for an order barring News Group journalists from revealing the identities of people involved.
She said the hairdresser had been employed by the public figure but was dismissed about a year ago.
The hairdresser has alleged unfair dismissal and sex discrimination.
Mrs Justice Simler said parties had agreed a "confidential settlement" of the dispute.
She said News Group wanted to write about the case, but the well-known figure wanted an order preventing names being revealed.
A spokesman for the Judicial Office, which provides support to judges, said the public figure had been given the go-ahead to take the case to the Court of Appeal.
The spokesman said an order barring the revelation of names remained in place pending an appeal court hearing.
He said no date had been fixed for the hearing.
Last week a celebrity who wants to keep his name out of a tabloid newspaper story about extra-marital activities won a Supreme Court fight.
Justices ruled that The Sun on Sunday should be barred from revealing the identity of the man, referred to in court as PJS.
They delivered a ruling after analysing the latest round of the man's dispute with The Sun on Sunday.
The man asked the Supreme Court to consider the case after losing a fight in the Court of Appeal.
Three appeal court judges ruled in April that an injunction barring The Sun on Sunday from naming him should be lifted, but a panel of five Supreme Court justices overturned that decision by a four to one majority and ruled the injunction should stay in place.
The Sun on Sunday wants to publish an account of the man's activities, but he argues that he has a right to privacy and has taken legal action.
He had sued News Group Newspapers, which publishes The Sun on Sunday, claiming that publication of information about alleged extra-marital activity would be a misuse of private information and a breach of confidence.
Any trial of those claims is likely to be overseen by a High Court judge, who could decide to lift the anonymity injunction after analysing evidence from both sides.