The Sun On Sunday wants to publish an account of the man’s alleged extra-marital activities.
However, earlier this year, Court of Appeal judges imposed an injunction preventing the tabloid from identifying the man after he took legal action.
Lawyers for News Group Newspapers, publishers of The Sun On Sunday, have asked appeal judges to lift the ban. They say the ban should go because the man — a showbusiness celebrity and public figure — has been named in articles abroad and his identity can be found on the internet.
The man has opposed the application and says the ban should stay in place.
Judges analysed argument at a Court of Appeal hearing in London yesterday and are due to announce their decision on Monday.
Detail of The Sun On Sunday case emerged in a ruling earlier this year following a Court of Appeal hearing.
Appeal judges Lord Justice Jackson and Lady Justice King did not identify the man in their ruling but referred to him only as PJS.
They said he was well known, married and in the entertainment business. They said his spouse — referred to as YMA — was also well-known in the entertainment business. They said the couple had young children.
Lord Justice Jackson said in the ruling that the man had appealed after a High Court judge ruled in favour of The Sun On Sunday.
Mr Justice Cranston refused to impose an injunction following a hearing in January — although he ordered a temporary block on publication pending the hearing of an appeal.
Lord Justice Jackson said he and Lady Justice King decided to allow the man’s appeal after balancing the man’s human right to respect for family life and the newspaper’s right to free expression.
A politician who used parliamentary privilege to expose football star Ryan Giggs as the celebrity protected by a privacy injunction said judges must lift the ban in The Sun on Sunday case.
Former Liberal Democrat MP John Hemming says the English legal system is in danger of looking “silly” if the bar stays in place.
“This isn’t a secret any more,” said Mr Hemming. “We have a situation where information has been published in the USA and in Scotland. People can find it on the internet.”
Mr Hemming hit the headlines in 2011 when an MP in Birmingham. He named Giggs after his name emerged on social media — who was the subject of a similar court injunction — when speaking in the Commons, knowing parliamentary privilege protected him from legal action.