Judges are considering whether a celebrity who wants to keep his name out of a tabloid newspaper story will be allowed to take his case to the Supreme Court.
Justices at the Supreme Court were considering the application on Tuesday, a spokeswoman said.
"A decision whether to grant, or refuse, permission is expected to be made by the end of the day," she said.
The Sun on Sunday wants to publish an account of the man's alleged extra-marital activities and argue that his name has already emerged online.
The paper won a victory on Monday when judges in the Court of Appeal ruled the injunction would be lifted - but not until 1pm on Wednesday in order to give the man time to make an application to the Supreme Court.
Desmond Browne QC, who headed the man's legal team, told appeal judges that he wanted Supreme Court justices to examine the case.
Mr Browne suggested that the Court of Appeal decision might lead to the "rule of the press" rather than the "rule of the law" and signal the death of the "celebrity privacy injunction".
Gavin Millar QC, who led News Group Newspapers' legal team, had told the three appeal judges: "The information which is the subject of the injunction has now entered the public domain, has been published widely and is freely and generally accessible in this jurisdiction."