DUP members of the powersharing Executive are divided on the location of a sports stadium to be used for soccer, rugby and Gaelic games.
Culture, Arts and Leisure Minister Edwin Poots prefers current plans for the development of the former Maze prison and has set a deadline of the end of the month for viable alternative proposals centred on Belfast.
However, his Executive colleague Nigel Dodds has said unionists would not tolerate development of the Maze if the plans include a conflict resolution centre involving the retention of one of the H-Blocks where 10 republican hunger strikers died in 1981.
DUP leader and First Minister Ian Paisley has voiced his personal opposition to the siting of a stadium in Ormeau Park near Belfast city centre.
"However it is dressed up, whatever spin is deployed, the preservation of a section of the H-Blocks - including the hospital wing - would become a shrine to the terrorists who committed suicide in the Maze in the 1980s," said Mr Dodds.
"That would be obnoxious to the vast majority of people and is something unionist people cannot accept. But that appears to be the prerequisite as far as Sinn Féin is concerned if a stadium is to be built at the Maze." Mr Poots, whose Lagan Valley constituency includes the Maze site, does not believe a Belfast location is viable.
Dr Paisley opposes development of Ormeau Park and the placing of the 35,000 stadium there. He says the location is too close to residential areas and to churches - including his own Martyrs' Memorial Church on the Ravenhill Road.
All three major sporting codes have approved the Maze plan, although there are concerns among the rugby fraternity that such a capacity would make their attendances look small. The GAA, on the other hand needs a larger capacity.
The Maze development, which the British government favours, would include hotels and conference facilities as well as commercial, equestrian and agricultural areas. The 2012 Olympics committee has suggested soccer games for the London Games could be played at the Maze.