Greenpeace says the Russian parliament, called the Duma, has introduced an amnesty bill that would free specific groups of people convicted of minor crimes.
The bill, drawn up by President Vladimir Putin, has passed its first reading, media reports.
In its current form, it wouldn't free the Greenpeace activists, including Australian Colin Russell, and journalists, dubbed the Arctic 30, who have recently been released from detention on hooliganism charges.
Listen: Greenpeace Australia spokesman James Lorenz explains the Russian court proceedings to Hannah Sinclair
But Greenpeace says some members of the Duma have called for the bill to be extended to all people - including those charged but not yet convicted of hooliganism and rioting.
The activist group says amendments to the bill must be tabled on Wednesday (NZT) and a vote is also expected.
Two New Zealanders, Jonathan Beauchamp and David Haussman, are among those charged with hooliganism after two members tried to scale an Arctic oil platform in September.
The 30 were originally charged with piracy, but those charges have been downgraded.
The amnesty in its current form would only apply to certain people, for example mothers and the elderly, and only pertains to convicted criminals.
Even if charges were dropped against the protesters, it may take months for a law to be enforced and they would still have to be granted exit visas.
If the charges remain, it is not clear if Mr Beauchamp and Mr Haussman will be allowed to come home while they await a possible trial.
The amnesty bill would enable the release of Nadezhda Tolokonnikova and Maria Alekhina, the Pussy Riot members serving two years on hooliganism charges for an anti-Putin protest.
Some commentators say the amnesty bill is likely intended to silence Western critics in the lead up to next year's Winter Olympics.
