The council focus will be on construction and design rather than the deal under which the Government agreed to gambling law changes in exchange for SkyCity meeting the $402 million construction cost.
SkyCity's proposal was chosen in 2012 above four other interested groups as the only one which carried the cost of building the centre.
A council spokesman said staff were reviewing the application, and a decision was expected late next month.
The decision on whether to publicly notify it could be made by staff, referred to independent commissioners, or made by a hearings panel which includes elected officials.
Public consultation would add another 18 months to the timetable, which is already behind schedule.
Green Party MP and gambling issues spokeswoman Denise Roche yesterday said the significance of the development, the impact on the city, its traffic and surrounding businesses were likely to require public consultation.
Ms Roche, a former Auckland City councillor and planning commissioner, said: "Eighteen months is a reasonable time for democracy. There's been no democracy or transparency around this deal from the get-go."
Auckland Mayor Len Brown, who supports the centre, wouldn't offer a view on whether the application should be open for public submissions.
A spokeswoman for Economic Development Minister Steven Joyce said he had been told SkyCity had worked to meet the conditions for a non-notified consent, enabling the centre to be built quickly.
Interactive: Slide the rule to see how the convention will affect the city skyline
A SkyCity spokesman said the company was waiting on the council's decision.
"The 12-month design and planning process has been rigorous and we believe has led to a great outcome," he said.
An assessment report for the convention centre, submitted with the application, said "adverse effects associated with the proposal will be avoided, remedied or mitigated and will be no more than minor".
The application reveals SkyCity's existing convention centre, next to the casino, is an integral part of the new project. It said that to meet Government demands, the new centre and the SkyCity Convention Centre "will at times be used concurrently by the same delegates attending a single conference".
The application documents reveal SkyCity's original plan to host conferences of 3500 to 5000 people has been whittled back to hosting conferences attended by 1500 to 3500 people.
The application also shows SkyCity believed it would attract five large conferences each year involving 1500 to 3500 people.
It believed it would gain another 20 conferences of 800 to 1500 people and 45 domestic conferences of 200 to 600 people.
The other options
SkyCity's proposal was chosen in 2012 over four other proposals:
The Edge A rebuild and expansion of the Aotea Centre and refurbishment of the St James Theatre in Queen St.
Ngati Whatua Using land at Quay St near the old Auckland railway station.
Infratil Waterfront centre at the far end of Wynyard Quarter.
ASB Showgrounds Development of its Greenlane site with a 450-room hotel.
View: Architectural Design Statement for SkyCity's Convention Centre:
View: Design assessment: