The Auckland-based airline has recently announced new services to two other Asian destinations - Vietnam's Ho Chi Minh City and Manila in the Philippines.
In addition to Chengdu, Carr said Air New Zealand had been eyeing Chinese cities including Chongqing, Wuhan, Wenzhou and Shenzhen.
"Clearly Chengdu is a massive catchment area and there is a lot going on there in the aviation space," he told the Business Herald at the airline's Shanghai office.
Carr said Air New Zealand had been operating the Shanghai service for 10 years and it had only recently become profitable.
"Chengdu feels like Shanghai 15 years ago," he said. "It doesn't feel like it's quite at the stage where you can go, 'That's a market that we want to be in'."
Carr said the airline, like many other New Zealand companies, was focussing on increasing value rather than volume in China.
"Chengdu, at the moment, looks like a volume play," he said. "However the announcements go in the next couple of days, you might draw your own conclusions."
Carr said Shanghai was the greatest immediate opportunity and there was scope to further increase the number of flights it operated to the city, although accessing "slots" at Pudong International Airport was challenging.
"We now have a competitor on Shanghai [China Eastern] and they are daily as well and yet the market has absorbed that level of growth," he said. "You kind of go, 'How much more is there?'"
A year ago today there would have been maybe 17 flights a week out of China to New Zealand - today there are 35 and it's low season.
Air New Zealand, he added, was positioning itself as a more premium offering than its China-based rivals.
"It's brutal out there, to be fair," Carr said. "There's been some pretty aggressive pricing - we've managed to keep ourselves a little bit above that."
The low season was particularly challenging.
"A year ago today there would have been maybe 17 flights a week out of China to New Zealand - today there are 35 and it's low season," Carr said. "I think we'll find our way through low season better than most. I suspect some of those [competitors] are going to be hit with some fairly lightly loaded flights in the coming months."
With China's economic growth slowing and concerns rising about the country's debt levels, he said it was important to listen to the "macro noise".
But the focus had to stay on the business.
"Then you get down to your customers and provided you understand where they fit within this macro-economic story, and their wealth position, then you can still execute," Carr said.
• Christopher Adams is travelling in China as a recipient of the New Zealand China Council Media Award.