Two weeks ago, Polestar announced that 58 jobs at its Leeds and Nottingham facilities were under threat.
However, Unite held a meeting with the print giant on Wednesday (28 July), at which a number of options were proposed that could reduce the number of planned job cuts.
National officer Steve Sibbald said: "If it is accepted by our members and the company, this proposal would dramatically reduce the redundancies.
"It includes elements such as a change of shift pattern that would give the company the cost savings they are looking for, while maintaining as many jobs as possible. It would be on a temporary basis, returning to normal once the company is headed in the right direction again."
A meeting is scheduled to take place this Wednesday (4 August), at which a decision from both sides is expected.
Polestar HR director Simon Jones said: "The consultation period has been very constructive. We have received a proposal from the employee side which the company is currently considering."