Transport Minister Simon Bridges said today that there was a possibility that light rail could be brought forward on the route. That was likely to depend on demand for train services.
"It could well be sooner rather than later, and I'm very open to that," he told reporters at Parliament.
His Government had already proposed the sort of land value capture that the Greens were proposing, he said. It might also seek funding from the airport and from Mt Eden businesses along the rail line's route.
"If we did a serious public transport project ... there would be other parties that would benefit significantly from that. Around the world ... they've looked at how they've managed to help fund the project through those sort of things."
Earlier this week, Bridges said it was possible that some infrastructure projects could be brought forward for 2021, when Auckland will be hosting the Apec political conference and possibly the America's Cup.
But it was not feasible to have rail or a bus corridor in place between the airport and the CBD by 2021, he said.
"Just the legal and land issues take us out to 2019. And that doesn't leave us much time."
He said the Government would consider upgrading sections of the route before 2021.
Route protection has already begun for a mass transit corridor between the airport and the city. The New Zealand Transport Agency (NZTA) and Auckland Transport decided in March that a busway corridor would be a "credible solution" for the next 30 years.
Over the medium to long term, there would be a staged transition to light rail.
Genter said the project could not wait 30 years.
"In that timeframe the number of passengers travelling to and from the airport will double and the number of people working near the airport will triple."
Once the project is completed, it will take 43 minutes to make the trip from the airport to Wyndham Quarter on Auckland's waterfront, via Dominion Rd and Queen St.