Mr Poots stressed that if the project were to be eventually withdrawn; locals would demand a more substantial scheme for the area.
However, he said his ultimate goal was to ensure a facility was constructed on the former Maze prison site, in his constituency.
The DUP assemblyman is the current Deputy Mayor of Lisburn City Council.
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He and Mayor Ronnie Crawford held a meeting with First Ministers Peter Robinson and Martin McGuinness, last week, to discuss the stadium issues.
Mr Poots told the Belfast Telegraph: "I'm always an optimist."
"We met the First and Deputy First Minister on Monday and the case was re-stated.
"There has to be something of reasonable significance there. If they step back from the stadium, we will be seeking something better than that.
"It's not a case of them walking away from a sports development at the Maze and us saying, oh dear, that's too bad.
"We will be aggressively fighting for something that is even more significant," he added.
Speculation has mounted that incumbent Sports Minister Gregory Campbell is set to axe the Maze plans, despite calls from construction industry representatives to deliver a project - in order to help sustain the local building sector.
(PR/JM)
