Ms Butler has held the federal seat for eight years and has a margin of 2.86 per cent on a two-party preferred basis.
However her primary vote has been falling steadily since 2014, while the Greens' share of the primary has risen more than 13 per cent.
Greens candidate Max Chandler-Mather said door-to-door polling of 25,000 voters conducted by his party showed he could benefit from a 7.2 per cent swing at the May 21 election.
That would put his primary vote just above the 31 per cent his Labor rival won four years ago.
Greens' polling has previously predicted it picking up a Brisbane council ward and two state electorates, and Mr Chandler-Mather is optimistic about the results.
"It's a confirmation that all of this hard work is paying off for us, and now we're just going to get our heads down and campaign like crazy for the next four-and-a-bit weeks," he told AAP.
However, Labor dismissed the Greens' release of polling data as an election stunt, and rejected the result.
"This isn't a poll. This is a Greens party hype campaign," a Labor official told AAP.
"It's part of their political strategy but that doesn't make it true.
"Terri and Labor volunteers across Griffith are working hard every day to take the fight to Scott Morrison and elect an Albanese Labor government."
Meanwhile, the Greens are gearing up for a stoush with the Brisbane City Council over restrictions on electoral yard signs, which it says are undemocratic.
Lord Mayor Adrian Schrinner, a Liberal National Party member, passed laws last year restricting federal signs on private property.
Under the rules, signs can be no larger than 60cm by 60cm, with limits of one per property and a maximum of 150 per federal electorate.
Mr Chandler-Mather said his party will ignore the laws, which he said deny thousands of voters their freedom of expression.
"A 150-yard sign cap on a federal electorate, which has about 120,000 residents, would allow less than one per cent of households to have a yard sign," he said.
"That is so obviously ridiculous."
Brisbane LNP Councillor Kim Marx said the law applies to all parties equally and will be enforced during the campaign.
"The law strikes an appropriate balance between allowing freedom of expression while preventing a political signage free-for-all that residents strongly oppose," she told AAP.
7°C