But Wellington Airport says there has been interest from other airlines.
Airport chief executive Steve Sanderson said he was not surprised Barnz did not know of international airlines with plans to fly to Wellington.
The airline industry was intensely competitive and association members were in many cases direct competitors, he said
"It is understandable Barnz is not aware of its members' routes strategies. It is common for airlines to avoid publicising their future route development plans."
And airport chairman Tim Brown, from 66 per cent owner Infratil, said he had expressions of interest in writing from airlines.
"We've had airlines in writing saying 'if we could we would'. I'm sure between now and the time people commit funding there will be a coalescing and growing transparency over those arrangements. For airlines to say they wouldn't be prepared to fly is nonsensical."
A 350m extension to the runway would allow widebody planes such as Boeing 787 Dreamliners to use Wellington on routes to Asia and North America.
The airport says that would boost tourism into the country and make it more convenient for travellers in the Wellington region. At the moment international services are limited to Australia and the Pacific Islands on smaller aircraft.
Councils, which own about one-third of the airport company, have allowed for $150 million in their long-term plans should the work go ahead.
A study done for the airport shows that extending the runway could yield $1.75 billion in direct benefits between 2020 and 2060 and $684 million for the Wellington area in the same period.
But Beckett said more study needed to be done.
"Committing millions of dollars of ratepayers' money to the extension of Wellington Airport's runway is premature," he said.
A cost benefit analysis - where the benefits are compared with what would happen without the extension - was required. An NZIER study commissioned by Barnz confirmed this.
"People in the Wellington region, who will fund a lot of the extension, deserve better," Beckett said.
He said it was not a matter of airlines being against the extension, but more about concern over the cost.
An Air NZ spokeswoman said that while supportive of a thriving, well-connected Wellington, the airline wanted to see a robust cost benefit analysis of the extension to be convinced that this was the best plan.
"We would also want to be reassured that customers who do not use the extended runway will not be asked to help pay for it," she said.
Brown said Infratil's financial contribution to any extension would be determined by the funding model arrived at.
"When push comes to shove you're going to have a very high level of investigation so that all the parties are comfortable that nobody is free riding on the deal. At that point you'd have to work out the allocations of who pays what."
Dogfight over runway
The plan: A 300m-350m extension of the runway at Wellington Airport.
The cost: $1m a metre.
Airport says: Necessary to encourage tourism to and from a fast-growing market. Incumbent airlines naturally oppose plans that allow rival carriers in.
Airlines say: No airlines are interested in flying widebody planes to the airport. More work needed to work out benefits of plans that will ultimately cost passengers.
