To avoid burdening local taxpayers, the Cardiff city council is hoping to find a private company to run both venues.
Nigel Howells, the council's executive member for the arts, told the Echo that the plan does not imply "privatization by the back door," adding that the council would always retain authority over programming decisions.
Cardiff Council has now advertised in the European Journal, inviting offers from private companies interested in operating and maintaining the two complexes, according to the paper.
John Sheppard, the opposition Labour Party's finance spokesman on the council, implied bad faith on the part of the majority Liberal Democrats, telling the Echo, "This is driven by the financial mess the council is in and not by the desire to retain these cultural facilities which are so important to the vibrancy of life in Cardiff."