DUP minister Nigel Dodds says a stadium at the former Maze Prison site would not be acceptable if the complex also contained "a shrine to IRA terrorism".
He said unionists would not support the project if the green light was also given for a conflict transformation centre retaining one of the H-Blocks.
In contrast, DUP leader Ian Paisley has ruled out rival plans to locate the stadium at Belfast's Ormeau Park.
And DUP culture minister Edwin Poots says a Belfast stadium is not viable.
A 35,000-seater stadium for soccer, GAA and rugby is planned for the Maze/Long Kesh site, but opponents argue the stadium should be built in Belfast instead.
Mr Dodds insisted he was speaking in a personal capacity.
"It is quite clear now the price for Sinn Fein support for the Maze project including the stadium is a shrine to IRA terrorism," said the North Belfast MP.
"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 (the republican hunger strikes).
"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 Fein is concerned if a stadium is to be built at the Maze."
Mr Poots, whose Lagan Valley constituency incorporates the Maze site, has given interested parties until the end of the month to put forward alternative proposals.
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