Last month, the high street retailer announced plans to close the schemes, citing a £41m deficit and high running costs.
Amicus said it has met with both WH Smith Retail and subsidiary Smiths News and tabled proposals on changes to their existing schemes in an effort to persuade the firms to keep them open.
Both companies said they would consider the proposals and further meetings have been arranged to discuss the plan later this month.
Ann Field, Amicus’ national officer, said: “We believe that we have a viable plan to keep the schemes afloat and one that our members and the companies can afford to sustain. We hope that they give it very careful consideration.”
Amicus represents more than half of the approximately 2,500 employees affected.