The owner of the plant, Ineos, announced its closure yesterday with the loss of 800 jobs and a potential 2,000 more among contractors.
Employees had rejected management proposals to end their final pension scheme and cut shift allowances. The company had argued that they had no alternative but to close the business after staff refused to accept their survival plan.
The plan included a pay freeze, ending of a final salary pension scheme and other changes to terms and conditions. Ineos claimed white-collar workers such as administrative staff had backed the plan, but workers represented by Unite had rejected it.
Unite said today it had made a number of recommendations to the owners of the business a union spokesman said: "Unite has made recommendations to Ineos as way to save jobs and prevent needless harm to this plant and the local community.
"We meet with the company today and will hear then if they share these objectives."
The company has said that despite the prospect of further meetings in the next few days to resolve the dispute there were "no prospects" of returning to conciliation service Acas to discuss the closure of the plant.
The dispute at the plant first flared up over the summer when the union disputed the treatment of a Unite official Stephen Deans a Grangemouth employee of 20 years.
Mr Deans was accused of trying to rig the selection of a Labour candidate for Falkirk, but was later cleared. Ineos had also carried out an investigation into Mr Deans which is due to report on Friday. Unite members had planned to strike last Sunday over the issue.
Tom Crotty, a director of Ineos, said the company would put Unite's proposals to shareholders if there was a "very significant" change from the union.
He told BBC Radio Scotland's Good Morning Scotland programme: "The management team on the site will listen to hear what Unite has said.
"If they believe there are substantive differences in where we are now then clearly they have a duty to take that back to the shareholders.
"The shareholders met after the vote on Monday and, quite understandably in my opinion, took a view that if the workforce had rejected that £300 million investment, then how were they going to go ahead and make it if the workforce were not behind that? That is why the closure announcement has been made.
"If the management team feel that there is a very significant change then I'm sure they would probably feel they would need to take that back to the shareholders and have further discussions."
Finance Secretary John Swinney told the programme: "I hope that at this very, very, very late stage in the process there is a willingness to listen to and to consider the proposals being put forward.
"Everybody is agreed that this plant has a strong future with the necessary investment and that is why the Scottish Government is wiling to be a player in that.
"We are now in a position at the very late stage of having the opportunity to have a discussion about some of the substantive issues that will affect the financial future of the plant and I hope that discussion this morning is constructive and successful."
Additional reporting by the Press Association