This would be in spite of expected productivity increases on the ports' current footprints.
In less than 30 years, a solution must be found, either in the existing location or elsewhere.
"It is hard to say with confidence what the world will be like in 30 years, but on current projections, [reaching capacity by 2040] is still likely to be true. We think we can accommodate container terminal volumes for 20-plus years, but certainly by 2040 our container terminal capacity is likely to be used up," said Ports of Auckland spokesman Matt Ball.
"After that, we either need to find other ways of increasing capacity on the existing footprint - and who knows what technology will be available in 30 years - expand the container terminal, or grow capacity at another port."
Waterfront Auckland general manager of development Rod Marler said there had been some thinking about how to use the ports' large space if industrial operations were to be phased out over the long run.
"It doesn't stop us thinking about it. We've got a lot of thinking around how those areas can be developed, but it isn't for public discussion at this stage. We're in the strategic space, so we're always looking at what the opportunities might be. So, yes. We have been thinking about it. But we're not putting that out into the public realm. We don't think going down such a controversial path is helpful at this stage."
In a presentation last November, Ports of Auckland chairman Richard Pearson said the viable long-term growth option was Marsden Point (of which the Ports own a partial stake).
The depth of its harbour and available land space meant it was the port that could most naturally handle the container ships of the future and their loads.
However, poor rail and road links would make it inefficient without significant investment.
Tauranga's port has some capacity to expand into, and Mr Pearson said it was important for meeting medium-term growth.
For Auckland, however, losing trade to Tauranga means losing some shipping business and dividends for the council.
The alternative ports study, which was done in 1999 but has not previously been released, looked at a sample of six representative coastal locations around Auckland.
They were all considered achievable, but ranged in cost and likely environmental damage.
A port in the Manukau Harbour was considered to be among the most expensive options due to extensive and continuous dredging required on its sandbar.
An option on the west coast, at Muriwai, was also assessed as difficult due to the high waves of the Tasman.
An offshore port near Ponui Island would see island wharves built in the Firth of Thames, connected by road and rail bridges. Minimal dredging would be required, and it ranked in the middle of the pack for cost.
The alternative ports were estimated in the neighbourhood of $3 billion for capital costs, including transportation links, when converted to 2012 dollars.
The Ports' report says staying in the city centre is cheapest and avoids environmental damage.
Still, the inner-city port has its own costs, including $1.7 billion in transport projects which would help move containers to an inland port in South Auckland where most freight is handled, according to Auckland Council documents.
A third rail to Papakura - which would put frequent long freight trains through suburbs - was estimated at $700 million by the council, and improved port access by road via Grafton Gully at $1 billion.
The campaign
This week, we examine the key issues in a campaign to break open Auckland's waterfront. This means:
1) opening up what's already there for everyone's use - particularly Queens Wharf, which is still far from reaching its potential;
2) looking ahead to more wharves being opened, notably Captain Cook Wharf; and
3) planning the entire waterfront - importantly, including ports land - as urban space, whether or not the working port is retained or developed.
Monday: What readers want on the waterfront
Tuesday: Auckland Architecture Association sketches the all-time good ideas
Yesterday: Tourism on the waterfront
Today: The working port and its vision for Auckland
Tomorrow: Where our city leaders stand