"I can't see it happening," he said.
After the meeting, Mr Dalton said while Napier may not need the multi-use facility it would be a good addition to Hawke's Bay's sporting infrastructure.
He said the Cambridge velodrome, which is just over three hours away by car, is used by elite cyclists.
"There is another level below that [the elite level] which they wanted to look after and foster," he said.
A Sport New Zealand spokesman said a Napier velodrome would be unlikely to be designed to compete with the Cambridge velodrome.
"The Avantidrome in Cambridge is the national training base while this would be more of a regional hub," he said.
Cycling New Zealand is trying to establish a network of these regional hubs, he said.
NCC chief executive Wayne Jack said the Cambridge facility was nearing its capacity in terms of its track usage.
He added that Cycling NZ has developed a cycling strategy that focused on road, mountain, BMX and velodrome cycling facilities.
He dismissed the notion that this new multi-use facility could go the same way as past projects like the wave pool, saying it was a completely different project.
"The wave pool was based upon a whole lot of information which was unable to be substantiated with the designer and the designer had underestimated it," he said.
The preferred location for the facility is adjacent to the Pettigrew Green Arena (PGA), which of late has been struggling financially.
"The PGA has struggled because in real terms it is a small arena with big arena overheads," Mr Dalton said. "And the recent management changes have been fantastic and it's looking much better than it has for a long time."
He said that the velodrome would not meet the same fate because there were "real efficiencies of scale".
"It [the PGA] simply has struggled in terms of its usage," he said. "There is a hell of a balancing act for all of those things to make them financially sustainable at the same time making them affordable for the communities.
"[But] if we put another facility alongside the PGA, there can be a sharing of staff."