Mid and East Antrim Borough Council is the subject of the legal challenge.
The case has been brought by a local resident.
A judicial review court heard the council's decision on complaints about the Woodburn scheme will be made on Monday, and issued by Tuesday.
Stop the Drill campaigners are seeking an injunction to stop the company behind the scheme, InfraStrata, from going ahead with exploratory oil drilling close to a reservoir that supplies drinking water to thousands of homes.
Permission for a judicial review was granted last week.
Protesters fear the drilling, less than 400m from Woodburn reservoir, could impact water supply to Carrickfergus, Larne, Newtownabbey and areas of Belfast.
But NI Water, which has leased the site to InfraStrata has said it is confident there is no threat.
The anti-drill campaign has been ongoing since February, but intensified this week after drilling equipment arrived at Woodburn.
On Wednesday, Friends of the Earth representatives from 25 countries suspended their AGM in Carlingford to join the protest.
On Monday, a protester was arrested after he climbed onto an oil drill headed for the forest.
The man had threatened to chain himself to the rig using a bicycle lock, but he later left it of his own accord.
He was arrested on suspicion of obstruction and released on police bail.
A key aspect of the controversy surrounding the drilling project is its progression under permitted development rights (PDR), meaning it did not have to submit a planning application.
In March, it was revealed this rule is to be looked at again by officials.
Environment Minister Mark H Durkan said he wanted to hear people's views about the use of PDR linked to oil and gas exploration.
Opponents claim the well got permitted development rights by default after planners missed a 21-day deadline to respond to the application with its views.
The Department of Environment said it decided the application qualified for permitted development status.
In February, Hollywood star Mark Ruffalo weighed into the dispute.
The actor who played superhero The Incredible Hulk wrote to the authorities in supporter of protesters.
A County Antrim council brought to court over a controversial oil drilling project outside Carrickfergus has said it will make a decision on complaints about the project next week.