The transport report is understood to recommend having 100 more buses on standby in case of a train failure.
More buses than the 30 provided on Friday would have been available had they not been required for peak services and school bus use.
Veolia has been directed to immediately put security staff on every one of its 140 carriages, improve security at all stations, have staff assigned to give on-board announcements, improve crowd management and have additional security staff at Britomart.
It is understood that about 370,000 people used public transport over a 20-hour period on Friday, compared to 240,000 on a normal weekday.
This figure was much higher than Auckland Transport had expected.
The council will also receive a report from Auckland Tourism, Events and Economic Development on the opening night celebrations during which 200,000 people poured into downtown Auckland, causing a crush outside Party Central at Queens Wharf which could only hold 12,000 people.
The Herald understands that most of the $2 million cost is for transport costs, but includes some additional costs for Government plans to expand Party Central at Queens Wharf along Quay St and to Captain Cook Wharf.
Rugby World Cup Minister Murray McCully has said the Government will pay some of the extra Party Central costs, but it not clear how much will fall on ratepayers.
The council is being asked to approve the $2 million with a view to recovering some of that money once the cup tournament is over.
Auckland ratepayers have contributed about $102 million to the cup, including $65 million on infrastructure and about $37 million in operating costs which included $2.7 million for the Friday night opening ceremony.
Auckland Transport has commissioned lawyer Chris Moore, a partner at Meredith Connell and Auckland branch president of the NZ Law Society, to make an independent inquiry into Friday's public transport meltdown.
Mr Moore has been given access to Auckland Transport files, contracts with service providers, and the power to quiz anyone involved.
His report will go to the transport board and will include an examination of possible penalties and compensation from Veolia.