Portadown Orangemen are seeking permission to challenge the secretary of state’s decision to ban the parade on a number of grounds.
They include the police assessment of the situation.
An emergency hearing took place at Belfast High Court on Saturday, but it was adjourned until Monday.
The Court of Appeal is also set to rule on Monday whether the Garvaghy Road Residents’ Coalition can contest the original Parades Commission determination allowing the parade.
Although Sir Chris subsequently banned it, he did not “strike down” the commission’s ruling, which still stands.
The court heard arguments in the case last week.
A lawyer for the residents’ group claimed the commission’s decision was flawed over how it weighed up the potential for disorder if the parade was permitted.