It's after the Christian-owned bakery was ruled to have broken discrimination laws by refusing to make a cake (below) with a slogan supporting gay marriage in 2014.
It appealed the verdict but the Court of Appeal rejected it earlier this year.
Ashers bakery then wrote to the Court of Appeal to clarify whether there were any more routes of appeal for them.
According to the Christian Institute, which is supporting the McArthur family who own Ashers bakery, the Court of Appeal said in a hearing on Tuesday that it could potentially launch another appeal in the Supreme Court through what the Institute called "a little known legal provision".
The court also asked the McArthur family's lawyers to provide written submissions "probably within the next week", according to the Institute.
At the hearing it was also said that the Attorney General, who intervened in their earlier case at the Court of Appeal, was seeking to refer the Ashers case to the Supreme Court "on devolution issues".
Simon Calvert, from the Christian Institute, said: "The family will be consulting again with the legal team before any further decisions are made but initial written submissions are required to be made and considered by the judges before anything else happens.
"It is the family's belief and ours that the recent ruling undermines democratic freedom. It undermines religious freedom. It undermines free speech.
"In addition to their own legal action, the Attorney General sought to refer the case to the Supreme Court for it to rule on his arguments about whether the laws that were used against the McArthurs are constitutionally valid.
"The family continue to be buoyed by enormous levels of public support and are grateful for the thoughts and prayers of their supporters."
