'I'd rather quit than back FG' - Wallace
Mick Wallace ruled out cutting any deal with Taoiseach Enda Kenny, saying he would "walk from politics" before supporting such a group.
The Wexford TD said meeting Mr Kenny was not top of his priorities and he "didn't have any burning ambitions" to meet with him.
Fine Gael, however, is unlikely to seek Mr Wallace's support and its negotiating team has instead spoken with other Independents.
Mr Wallace also appeared to rule out doing a deal with Fianna Fáil and other parties that had been in government.
He added he would "absolutely love" to be in government.
"Would I like to be the first Minister for Housing? It would be an absolute dream for me," he said.
"But would I work with a neoliberal grouping? No I wouldn't, I couldn't. I think I would have to take responsibility.
"I would have to walk from politics before I would work with a neoliberal grouping."
Mr Wallace spoke yesterday after a Red C survey revealed that six out of 10 Irish people want neutrality protected in the Constitution.
He said Ireland should "refuse to allow Shannon Airport to be used for any military purposes" but did not believe a deal with Enda Kenny would resolve the issue.
"Would it bring it any closer? Do I think that Enda Kenny would ever actually take a responsible decision and stop the US military use of Shannon, where we have facilitated untold slaughter in the Middle East? I don't see him changing his position in that area, no."
Mr Wallace was joined by Clare Daly, who said she did not believe Mr Kenny "will change his tune".
"If I were to talk with them, would we raise this issue? Yes, of course. But they haven't asked us," she said.