Michelin staff have been in discussion with bosses in attempts to agree pay-offs ahead of the closure of the company's plant in Ballymena.
The firm is withdrawing from the site, with 860 jobs being lost in the process.
Some workers claim they have been offered redundancy packages calculated on four-and-a-half-weeks' earnings for each year worked, as well as add-ons.
But some are thought to be reluctant to accept the offer on the table, and it is understood a union vote will take place.
A staff member told one newspaper: "People were expecting a bit more for the years they have put in. We will have to see what the add-ons are. Six weeks for each year seems fairer to most."
A Michelin spokesperson said: "We are in the process of completing a 90-day consultation with our employees.
"At this stage we are presenting the conclusions of that consultation, but until all the details are finalised and agreed we cannot say anything further.
"Our focus continues to be on the wellbeing of our staff and exploring all options to help them to find employment when the time comes."
Employees in Ballymena have been offered the option to relocate to the company's other European sites, including those in Dundee and in France.
Michelin announced in November it was to close down in Ballymena in 2018 after 48 years in the town, which was once regarded as a strong centre for Northern Ireland industry.
It blamed high energy costs, cheap Asian imports of tyres and falling demand for its products for the decision.
Meanwhile, Michelin last week claimed that it was not in discussions with the drinks company Bushmills over the future use of its site.
Reports suggested Bushmills had visited the location with a view to using it when Michelin leaves in 2018.
But a spokeswoman for Michelin said: "Michelin is not in any ongoing discussions with Bushmills or any other company."
The loss of Michelin is the latest in a series of major blows to Northern Ireland's manufacturing industry and, in particular, to Ballymena itself.
In 2014, the tobacco firm JTI Gallaher, which employs 700 people in the Co Antrim town, revealed that it would be shutting its doors in 2017.
Ballymena once enjoyed a reputation as Northern Ireland's manufacturing powerhouse, with workers at both Michelin and JTI earning well over the private sector average.
Following Michelin's announcement and other job losses in Northern Ireland manufacturing at the end of last year, the Enterprise Minister, Jonathan Bell, set up an advisory group to report on the challenges facing the sector, including energy costs.
It is scheduled to report back in March.
Other manufacturers have also made job cuts in recent months, including Caterpillar NI and Schrader Electronics, both in Co Antrim.