Unite has fiercely fought the plans since CUP announced that a 90-day consultation process had begun on the 22 January with staff at its UK printing arm – Cambridge Printing Services.
Today, CUP said that, while talks were ongoing with the union, early figures suggested "nearly half of the 119 or so previously threatened positions may be retained".
Options being explored by CUP include possible redeployment for some of the affected staff. It is also considering maintaining the print operations from other parts of its publishing arm until other solutions can be explored.
Peter Davison, corporate affairs director at CUP, said: "Our main aim at this time is to work with our staff and their representatives as closely as possible to minimise the number of jobs that have to go.
"We have had some very constructive discussions so far and we look forward to working with them until the end of the consultation to ensure that we get the best possible deal both for our staff and for the business."
Unite will outline the latest proposals, put forward by management at CUP, when it meets affected staff on Friday.
The union has met with the university's governing body several times this week, continuing its opposition to the proposed cuts.
CUP has argued that more than 80% of its work is now produced for overseas markets and that the printing division, which has a 425-year-old history in the area, "is unlikely to make a profit in its current form".
Unite national officer Ann Field said: "Our members have been buoyed by the extent of support from the Cambridge community and we continue to make the point that CUP is still a profitable organisation with a hard-working and dedicated work force."
Previously it has been announced that around 150 jobs across the print and publishing division could be affected by the consultation.
Also see:
Unite to meet with CUP bosses to discuss job cuts
CUP workforce to plead case to Syndicate over job cuts