Senior Greens have signed a joint statement urging Zack Polanski to consider giving Labour a clear run in the Makerfield by–election.
Former party leaders and councillors warned the contest must be approached with 'trepidation' – as Andy Burnham's appointment could offer a 'unique opportunity' to reform the voting system.
It follows calls to 'Unite The Right' and stop the Greater Manchester Mayor from returning to the Commons, paving the way for a Labour leadership contest.
The first survey of the by–election last week showed the vote on a knife edge – putting Mr Burnham on 43 per cent and Nigel Farage's Reform UK close behind on 40 per cent.
The Green letter, signed by the likes of former party leader Jonathan Bartley and ex–councillor and author Rupert Read, states: 'Greens have always put their values and the climate and nature first. Which is why we approach the Makerfield by–election with some trepidation.
'If Burnham will commit to backing proportional representation for the next general election Labour manifesto so that it is in place by the election after next, then on this unique occasion we don't think Greens should run a full campaign against him.'
Senior Greens have signed a join statement saying Zack Polanski (pictured) should consider giving Labour a clear run in the Makerfield by–election (file image)
The Green letter was signed by former party leader Jonathan Bartley (pictured) and ex–councillor and author Rupert Read (file image)
The first poll of the contest put Labour on 43 per cent support, with Reform on 40 per cent as Andy Burnham (pictured) bids to return to the Commons
The letter admits Makerfield is 'not a seat the Greens can win' – adding 'it will be a straight fight between Labour and Reform', The Sunday Times reports.
A proportional representation voting system would allow for a closer reflection of smaller parties' votes in Parliament.
Last week Mr Burnham said the current first–past–the–post system should change to enable 'less point–scoring, more problem–solving' and make politics 'more place first rather than party first'.
The comments were welcomed by Mr Read who said he hoped the Greens would not 'move heaven and earth to stop [Burnham]' if he committed to electoral reform.
Former Reform MP Rupert Lowe's party Restore Britain was predicted in last week's Survation survey to win 7 per cent of the vote – while the Conservatives were on 2 per cent.
Meanwhile the Lib Dems have been placed at 4 per cent and the Greens at 3 per cent.
Mr Farage said the findings exposed a 'two–horse race' in the Brexit–backing seat.
'Robert Kenyon is the only candidate who can stop Andy Burnham. This is a two–horse race – nobody else comes close,' he said.
Nigel Farage said the contest was a 'two horse race'. Reform's candidate is Robert Kenyon, left
While Mr Lowe last week trumpeted an endorsement from Elon Musk, Conservative leader Kemi Badenoch has ruled out 'any deals' with Reform.
The parties were ramping up their efforts over the weekend, with less than a month until the vote on June 18.
The Greens previously ran into issues with their candidate Chris Kennedy who quit after 12 hours for 'personal and family reasons'.
It followed the revelation Mr Kennedy had circulated an Instagram video referring to the arrests of two men over arson attacks on Jewish ambulances as 'total bulls*** to keep the false flag flying'.
The tightness of the Survation poll numbers reflects a big personal bounce for Mr Burnham. Without him as the candidate Labour was seen as losing to Reform by an 11 point margin.
Over the weekend, former Conservative cabinet minister Jacob Rees-Mogg told the Daily Mail the message from the figures was 'if you want Andy Burnham to be Prime Minister, vote Restore'.
'It looks as if Conservative voters have decided to vote tactically,' Sir Jacob said.
'They clearly think that avoiding hard-Left Burnham - or flip-flop Burnham, whichever you prefer - is more important than their historic loyalties. And Restore voters don't.
'Voting for Restore is a waste and it's bad for the country.'
On Friday Mr Burnham painted his bid to return to the House of Commons as an opportunity to get rid of Keir Starmer.
He said victory would mean 'changing Labour', with the widespread expectation he would mount a quick challenge for the keys to No10.
But Mr Burnham has been coming under increasing scrutiny over what direction he would take the Government.
He has already backed off his pledge to rejoin the EU - a view popular among MPs but regarded as deeply unhelpful in an area that heavily endorsed Brexit.
Mr Burnham was believed to have told Home Secretary Shabana Mahmood he supports her tough immigration crackdown.
However, he has now wavered on whether changes to indefinite leave to remain should be retrospective - regarded as crucial for addressing the wave of arrivals from recent years.
Critics have also accused Mr Burnham of watering down his commitment to a proportional representation voting system.
The Green Party told the Sunday Times: 'We respect all views from within the party on this issue. As a democratic party this is a decision for local members and a democratic candidate selection process is currently underway.
'We are not aware that Andy Burnham is ready to make, or indeed has the authority to make, any kind of deal. The people of Makerfield deserve to have a choice about who they feel best represents their interests.'