Unite may concede on most of the pay and conditions proposals put forward by owner Ineos in a late offer aimed to break the bitter stand-off.
Hours after Ineos delivered the devastating news that the plant was to close, on what was branded a black day for Scotland's economy, efforts were ongoing to turn back the clock with last-ditch talks held in Edinburgh and Whitehall.
And it has emerged the union is prepared to climb down over fears about the mass redundancies.
As reported in later editions of yesterday's Evening Times, the news that the petrochemical site was to close was broken to the 800-strong workforce at a meeting at the plant yesterday morning.
Union bosses and workers reacted angrily to the devastating blow, accusing Ineos of "economic and industrial vandalism".
The latest development comes amid fears that the knock-on effect of closure will affect the futures of 2000 other people working for contractors and other firms supplying the site with goods and services.
Grangemouth's adjoining oil refinery will remain open, but the company said it had not yet decided when to restart production after the site was closed last week because of the dispute.
There are fears the latter's closure would impact on the BP-owned Forties pipeline and its Kinneil processing facility, which is powered by Grangemouth.
It carries oil direct from the North Sea to the Cruden Bay terminal in Aberdeenshire before transferring it south to Kinneil.
Alex Salmond last night spoke for 30 minutes with Ineos chairman and chief executive Jim Ratcliffe and Unite in an attempt to reverse the "catastrophic" decision to shut down the petrochemical plant.
The First Minister claimed there was plenty of scope for both sides to back away from that catastrophe, amid suggest-ions Unite may have tabled a late offer to avoid the closure of the petro-chemical plant.
Meanwhile, tens of millions of pounds in UK taxpayer's money could be on offer to any potential buyer of the Grangemouth chemical plant from home or abroad, the Scottish Secretary has revealed.
Alistair Carmichael said the UK Government was at every level actively seeking to get a buyer for Grangemouth.
The Treasury, the Scotland Office, UKTI - the investment arm of the Foreign Office - and the Business Department were all now engaged in trying to save the threatened Scottish jobs.
Mr Carmichael said: "Prior to the announcement, the UK Government was already engaged through the Treasury in the process of infrastructure loan guarantees.
That is an offer that would be open to any potential owner of the chemical plant at Grangemouth.
UNTIL we know who is out there, who might be interested in taking it on, we can't say what would be available."
The Secretary of State said he had spoken to his Liberal Democrat colleague Vince Cable, the Business Secretary, about securing a new owner, adding: "We will work with UKTI, the Scottish Government and anyone else. Anybody who has a positive contribution to make in keeping these jobs at Grange-mouth will find they have a friend in the UK Government."
Earlier, Unite said it had made new proposals in a "last-ditch" effort to save the site, while the Scottish Government issued a fresh appeal for the two sides to hold talks to resolve the crisis.
The union's Scottish Secretary Pat Rafferty said workers were shaken by yesterday morning's announcement, adding: "Unite and our members at Grange-mouth are devastated by the announcement of the closure of the petro-chemical plant.
"It has confirmed our fears that this was the intention of Ineos all along.
"We have made further proposals in a last-ditch effort to stave off these catastrophic job losses, which we believe is tantamount to economic and industrial vandalism.
"Make no mistake - one man is holding this workforce and this country to ransom and that man is the Ineos owner Jim Ratcliffe."
This was echoed by Grahame Smith, general secretary of the Scottish Trade Union Congress.
He said: "The behaviour of Ineos is simply disgusting.
"And it reveals the true nature of a feral private equity concern that clearly believes it has no social obligations whatsoever.
"In anticipation of this eventuality, the STUC has been in discussion with Scottish Ministers and the Secretary of State for Scotland over the past few days.
"If Ineos is not willing to invest in this plant alter-natives must be quickly and diligently pursued.
"As many have noted over the recent period, the Grangemouth complex is too important to the Scottish economy to be closed on the vindictive whim of an unaccountable billionaire."
AS ONE worker left the meeting announcing the closure, he said: "I feel sick. It's gone. There are no livelihoods left.
"We don't even know if we are going to get redundancy out of it. I hope they are happy with themselves.
"It's gubbed. Everything's gone."
Appearing close to tears, the worker, who did not wish to be named, said he could only listen to about 10 minutes of the meeting, before he felt he had to leave.
He added: "There are folk in there have a husband and wife work here.
"That's it. Folk will be lucky if they have a house at Christmas."
Another member of staff claimed Grangemouth Petrochemicals chairman Calum Maclean had been "smiling" when he made the announcement.
Mr Salmond said the closure decision was, "hugely disappointing" and met with ministers for an emergency cabinet meeting yesterday to discuss the on-going situation.
After the meeting he vowed to continue discussions with management and unions.
He said: "This is the outcome that matches our worst fears which is why we urged getting the plant fired up instead of lying cold.
"The Scottish Government strongly believes the site has a positive future."
"We will continue to work with the UK Government and all other parties concerned to find a solution."