The Communications, Energy and Paperworkers Union says it only learned of the company's final offer for employees at the Stadacona mill through the media on Friday.
Operations at the mill have been suspended since November and White Birch now says the mill will be closed permanently unless the company can significantly lower salary, pension benefits and other costs.
The union's Quebec vice-president Renaud Gagne says members will meet in the coming days to determine their next steps.
The union and the company haven't given details on the company's latest proposal.
Greenwich, Conn.-based White Birch was the second-largest newsprint manufacturer in North America when it filed for bankruptcy protection in February 2010.
At the time it had about 1,300 employees companywide at three pulp and paper mills and one saw mill in the province of Quebec and a fourth pulp and paper mill in Virginia, operated by its Bear Island subsidiary.
When production at Stadacona mill was suspended in November, White Birch said the operation wouldn't be able to survive in the long term unless it got costs down.
Company president Christopher Brant has said acceptance of the company's final proposal is essential for the mill to resume operations.
The company manufactures high quality newsprint, directory paper and paperboard at mills in Canada and the United States.
A switch to digital forms of publication has eroded demand for paper used in newspapers and directories. Rising energy prices, a strong Canadian dollar and low returns for company pensions have also raised costs for the industry.