LGBT campaigner Gareth Lee is seeking to challenge the UK Supreme Court over its unanimous decision in favour of Ashers Baking Company.
It would appear Mr Lee wants the European Court of Human Rights to consider narrow aspects of the ruling. Such a legal process could take years and may not result in judges hearing the case.
The Christian Institute, which has supported Ashers throughout, said the latest legal challenge was unlikely to overturn the central aspect of the Supreme Court judgment.
Ashers Baking Company is owned and run by the McArthur family, who are Christians.
In 2014, they turned down Mr Lee’s order for a same-sex marriage campaign cake. The McArthurs took the decision because the message on the cake conflicted with their Christian belief that marriage is between a man and a woman.
But the taxpayer-funded Equality Commission for Northern Ireland pursued them through the UK courts.
The judgment in favour of Ashers was welcomed by lawyers and commentators from across the spectrum because it protects people of all views.
In October last year, the Supreme Court found in Ashers favour, saying the family’s objection “was to the message, not the messenger”.
Media reports today suggest the focus of the appeal is the political discrimination element of the ruling. That specific law only applies to Northern Ireland.
Mr Lee is not taking Ashers to court, and the Equality Commission for Northern Ireland is not backing the case.
He is instead being represented by Phoenix Law’s Ciaran Moynagh, who claimed the Supreme Court “created legal uncertainty” with its decision.
The European Court of Human Rights is not a European Union institution, meaning any court case would be unaffected by Brexit.
Simon Calvert, a Deputy Director at The Christian Institute, said: “The judgment in favour of Ashers was welcomed by lawyers and commentators from across the spectrum because it protects people of all views.
“I’m surprised that anyone would want to overturn a ruling that protects gay business owners from being forced to promote views they don’t share, just as much as it protects Christian business owners.
“Judges at the UK’s highest court could not have been clearer in their decision: Ashers’ objection to the cake was to the message, not Gareth Lee himself.
“From what we know so far, we do not believe there is a real danger of the substance of the judgment being overturned.”