Some €20m in State funding was sanctioned for the project just over two years ago, and Taoiseach Enda Kenny turned the sod ahead of the 2016 general election.
However, the project has stalled over internal design issues, and become mired in controversy over the delays and associated rising costs.
It emerged earlier this year that while plans for a 10,600sq m facility won the tender for the initial state funding, increased state funding would be required to deliver a larger 13,500sq m facility to make it commercially viable.
BAM told councillors at a closed-door briefing in February that the costs had risen by €12m and a €6m contingency would also be required, given that design work was not finished.
But Lord Mayor Des Cahill and Fianna Fáil councillor Terry Shannon said it was their impression after the briefing that BAM would cover the contingency costs.
“It is now clear that the costs associated with the project are spiralling out of control,” Mr Shannon said.
“Everyone knew the funding model when we signed off on the original tender... But they [BAM] seem to be coming back for seconds, thirds and fourths. It wouldn’t be allowed in any other tendering process.”
BAM was not available for comment last night.
Cork City Council has submitted the company’s request for extra funds and an economic evaluation report to the Department of Arts, Heritage and the Gaeltacht. It will then be sent to the Department of Public Expenditure for a decision.