Greens leader Adam Bandt, who is leading negotiations with the government, is pushing for the 43 per cent reduction by 2030 to be increased, but Labor is remaining steadfast on its target.
Mr Bandt will take negotiated concessions back to the party room on Monday, Tuesday and Thursday ahead of a proposed vote in the lower house after the final meeting.
"There'll be a vote before the end of the week," he told Sky News on Sunday.
"We'll have the discussions and I'll take a position back to my colleagues.
"The party room will ultimately get the say about how we vote in the (lower) house and how we vote in the Senate."
There remains the chance the bill will be postponed in the lower house until parliament sits again in September.
But Climate Change Minister Chris Bowen has expressed his intention to have legislation passed this week to come before the Senate the following month.
Whether any Greens amendments will be moved in the lower house, where the government holds a majority, or the Senate will also be a topic of discussion.
The Greens hold the balance of power in the Senate, where the government needs the minor party and one extra vote to pass legislation the opposition doesn't support.
"Part of the reason we saw the Greens vote go up at this election is people want us to work constructively with the new government but to push them to do better," Mr Bandt said.
"That's the approach we're taking and it's going to have to be a parliament where everyone gets a bit.
"The whole 'it's my way or the highway' politics has been rejected by the people at the election."
The Greens are also pushing for a moratorium on new coal and gas projects, something the government has ruled out.
"If on the one hand you're passing legislation ... one week to say let's talk about cutting pollution ... then the next week you start opening up the Beetaloo basin or any other projects, you could blow that target out of the water," Mr Bandt said.
