The GAA would not agree to a proposed multi-sports stadium being built in Belfast, Sports Minister Edwin Poots has said.
Mr Poots said the GAA had ruled out proposed stadia on both the Belfast North Foreshore site and the Titanic Quarter.
Gaelic sports, soccer and rugby would be played at any future stadium.
Plans have been drawn up for a 35,000-seater facility at the Maze site, near Lisburn in County Antrim.
Mr Poots said the Irish Football Association was open to various sites, but its chief executive, Howard Wells, had a personal preference for the Maze, which is a former prison.
The minister told the assembly's culture committee that rugby authorities favoured a Belfast site.
"Ultimately no unionist will accept any proposal which will be a glorification of terrorism"
Assembly members interrupted their summer recess to address the controversial matter.
Mr Poots told the committee that consultants had begun work on a final business plan.
This would focus on a number of options including an economic appraisal of the Maze proposal, the "virtual Belfast" option and a cost analysis of refurbishing existing sporting venues.
Ulster Unionist committee vice chairman David McNarry asked the minister what impact unionist indignation would have on his decision on whether to take forward the Maze stadium plan.
Mr Poots said that while the issue of the conflict transformation centre was a matter for another department, "ultimately no unionist will accept any proposal which will be a glorification of terrorism".
He said cross-community consensus was essential.
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