Detailed budget proposals will be drawn up over the coming months, with the final budget to be agreed next March, the Local Democracy Reporting Service said.
The venue element of the wider scheme was placed under review early last year.
Opposition groups had urged the then-Labour administration to scrap the plan but the council said there was still demand for a venue.
The wider development scheme has a budget of more than £200m.
At a meeting of the council’s Growth and Regeneration Panel on Monday, questions were also raised about the future of the Queen Street plot – another aspect of the Our Cultural Heart scheme.
That site was once earmarked for a new STEM block for Greenhead College, but funding could not be secured.
The council is now considering alternative uses, including a hotel, offices, a car park or housing.
The meeting was told how the scheme had already delivered a new library hub and public square, with the only remaining element of the first phase being the food hall on the site of the former Queensgate Market.
Although not open yet, the building has undergone a major transformation and is now at the stage where the council is seeking food businesses ahead of a planned launch next year.
