The job will take about five years and involves building a 5km motorway to link Auckland's Western Ring Route to State Highway 20, enabling a direct connection to Auckland International Airport via the two motorways.
Leighton also wants to score the valuable Wiri men's prison job and is bidding for that in the GLM consortium with Mainzeal and operator G4S.
That puts Leighton directly into the territory of Hawkins Construction and Fletcher.
The prison job is far more valuable than just a build: it includes ongoing management and maintenance and is the first public-private partnership prison job to run in New Zealand.
The Corrections Department wants a new men's prison on land adjacent to the Auckland women's prison at 20 Hautu Drive in Manukau. Parties short-listed for the job are:
* GLM Consortium: G4S Australia and New Zealand Limited, Leighton Contractors and Mainzeal Property and Construction.
* Secure Future Consortium: Serco Australia, Fletcher Construction; Spotless Services NZ, ACC and John Laing Investments.
* NZCS Consortium: The GEO Group Australia, Hawkins Construction, Honeywell and Capella Capital.
Leighton has been in New Zealand for more than a decade, first working on the Central Motorway Junction and then the Northern Gateway Toll Road from Orewa to Puhoi as part of the Gateway Alliance.
Jones says the planning and resource consent processes for the Northern Gateway project were difficult. Based on his experiences in Australia, Sullivan said it takes longer to get projects completed in New Zealand.
Jones said Alpurt has been finished but only now are designs being considered for the motorway extension north of that highway.
"That's probably different to how they would do it in Australia where rather than piecemeal, they would get the corridor secured first so if they wanted to carry on, they would not have to wait.
"There would be a lot more focus on getting the corridor secure early," Jones said.
Both men praised the $1.8 billion Waterview connection planning process, saying this was a model for future projects.
Leighton has grown from employing about 350 staff and contractors here two years ago to about 700 people now.
The business is one of Australia's biggest contracting and infrastructure outfits, with A$9.6 billion work in hand, employing 12,000 people here and in Australia. It is also involved in the Middle East, South Africa and Asia.
Sullivan said the business wanted to win more work and expand significantly in New Zealand.
"We've been in investment mode, building up capability.
"We've put many millions of dollars into projects and the company is committed to working here, growing and diversifying away from transport into energy, for example power stations in Southland and on the West Coast, also irrigation schemes in Canterbury and the Hawkes Bay.
"We can differentiate ourselves through our expertise in the public private partnership market here," he said, adding that was one of Leighton's strengths in Australia.
Business development manager Andrew Maclean said that a few weeks ago, a consortium which included Leighton had won the A$1.8 billion PPP contract to build the new Royal Adelaide Hospital on North Terrace in the heart of the CBD.
The South Australian Government said construction was set to start later this year and is scheduled to be completed in 2016. The new hospital will replace the existing Royal Adelaide Hospital which opened in 1840. "The new Royal Adelaide Hospital will be the state's flagship public hospital and also its biggest."
Who to pick
* Leighton Contractors (lead) with John Holland, Fulton Hogan, AECOM, SKM. Sub-alliance partners: UGL and Keller
* Fletcher Construction (lead) with McConnell Dowell, Obayashi, Parsons Brinkerhoff NZ, Beca Infrastructure and Tonkin & Taylor.