The identities of the celebrities named as PJS and YMA in court documents could be revealed on Thursday, it has been announced.
The Supreme Court said on Monday that the hearing would begin at 9.30 on Thursday 19 May, when it would be streamed live.
The Court postponed making a decision on the celebrity threesome injunction at the end of April.
The Court of Appeal said the injunction should be lifted, saying it was no longer viable in light of easy it had become.
But it issued a stay that allowed PJS to appeal to the Supreme Court, which he did.
The press is currently still unable to name the celebrity, who allegedly had sex with another couple, and his world-famous spouse, at the centre of the legal row.
The injunction is only in place in England and Wales and many publications around the globe have identified the pair.
An Australian news website, a Scottish newspaper and a UK political blog are among those who named the pair.
The injunction was originally granted in January and remained largely unknown until a US magazine’s publication of their identities triggered a backlash in the press.
The case has reignited the thorny debate over what constitutes “in the public interest” with newspapers passionately arguing that British law is not keeping up with “the age of the Internet”.
Pressure continued to mount after the identity of a married actor who reportedly had sex with Helen Wood was revealed by US media and on Twitter.
It’s alleged that the married actor paid for sex with Wood, 30, the former escort who once claimed she had an affair with England footballer Wayne Rooney, while his wife Coleen was pregnant with their first child.
British media are still gagged from revealing the A-lister’s identity, even though the ‘family man’ actor was named by US media earlier this month and on social media including Twitter and Facebook.