It suggested it may stand down in Plymouth Sutton and Devonport to give Labour a better chance of winning the seat from the Tory MP Oliver Colville.
In return it wants Labour to agree not to contest the Totnes seat.
Dr Sarah Wollaston, Conservative MP for Totnes, described the plans as "anti-democratic".
The Green Party said it was "early days" but it hoped arrangements could be made locally with the Labour Party.
More on the pact story, plus more Devon and Cornwall news
It follows a letter from the party's leadership to Labour leader Jeremy Corbyn and Liberal Democrat leader Tim Farron for similar deals around the country.
Dr John Green, South Devon Green Party chairman, said: "I think people want a Parliament elected that better represents the views of the electorate.
"I believe our voters would prefer some sort of progressive alliance that would ensure the Tories don't have a majority in the next Parliament."
Plymouth Sutton is the most marginal seat in the South West. It is traditionally a Tory-Labour contest. The Conservative defender Oliver Colvile held on in 2015 but by just 523 votes.
The Greens got more than 500 votes so the logic is pretty obvious.
Arguably the perfect seat for this is St Ives in Cornwall which was Lib Dem from 1997 to the last election.
There the Green vote alone, had it switched to the Lib Dems, would have seen the Lib Dem holder hold the seat.
And the previous Lib Dem MP Andrew George has done lots of campaigning with the Green Party's Caroline Lucas, so there could be a perfect fit there.
Mr Colvile said: "I was the underdog in this constituency and I'm not going to try and pre-judge what would happen if there was a deal."
Luke Pollard, Labour's election co-ordinator for the ward, said the party was "fighting to win" and he was not aware of any contacts for a pact with the Greens.
"I was as surprised as anyone when I heard about it," he said.
Dr Wollaston said: "It looks anti-democratic" for a "small group of people dividing this up between them".
Devon County Council's Liberal Democrat group has an arrangement where five councillors have an alliance with two Greens.
The local Lib Dem leader Keith Baldry said it would be "up to local constituencies" to make any decisions for the general election.
"Locally it could be a good idea and we will take part in any talks to do the best for the area."
The Green Party has said it may not field parliamentary candidates in some seats in Devon in a tactic calculated to help prevent a Conservative victory.