Napier mayor Bill Dalton said this had been the city council's only approach, "at which stage they said not now and but it wasn't a final no".
"We've pulled the project off the agenda at the moment while we do a little more work but our intention would be to go back and visit the regional council once we've got all the work done," he said.
However yesterday Mr Graham said the regional council's sentiment was that their funding needed to be focused on environmental issues.
"I have canvassed various councillors on their thoughts on the matter and I think it would be very unlikely that we would be able to support the [multi-use facility]," he said.
"Its not that we don't want to, we'd love to give everyone money again but we're not in a position to".
The regional council has granted funds to regional projects in the past - including the Hawke's Bay Regional Sports Park, and MTG.
However Mr Graham said he did not think the council saw "ourselves in a position to do that again" as there were a number of environmental problems facing the regional council which "are going to require a substantial amount of capital to fix".
"I think there's a sentiment around the council to stick very closely to our core competency and get those things right," he said. "Without putting it to the council in my view they need to focus on their core competencies which are huge, we have huge challenges in front of us."
Mr Dalton said he agreed it was "highly unlikely" the regional council would provide funding in light of these issues, "but that wouldn't stop us asking".
Hastings mayor Lawrence Yule has also spoken about the proposed facility, saying if council decided to progress to the next phase the Hastings District Council would want to be consulted.
The proposed site of the facility is at Pettigrew Green Arena. When the stadium was initially built, the district council made a $1million contribution.
Despite being a third shareholder in the stadium, Mr Yule said they had not been "formally asked" by the city council about the project.
"What we're interested in is what impact its going to have on the PGA, who's going to liable for extra operating costs and potential maintenance costs of the velodrome and what they're building," he said.
"If its going to have a material impact on the PGA we do need to understand that and I imagine EIT would be in the same position."
The mayor said he imagined if the city council proceeded with the project, they would discuss these issues with the other shareholders.
Mr Dalton said this was always the intention, but council had been waiting until there was "something firm" to put before the shareholders.