The printing and publishing business, which has a 425-year-old history in the area, entered a 90-day consultation period with staff in late January with its printing division Cambridge Printing Services bearing the brunt of the job cuts.
Tomorrow Unite, which is in discussions with the company, is set to rally against the proposed cuts at the Guild Hall in Cambridge.
CUP has said it will give one-to-one support and advice to those finding new jobs.
In addition to training and assistance in writing CVs, the affected staff are eligible to have paid time off in order to go to job interviews.
Stephen Bourne, chief executive at CUP, said the move "has been an incredibly difficult decision for all concerned".
He added: "Since April 2008 we have been looking at every other option for making our printing business more profitable, but the long-term changes in the industry, and the future forecasting we have done, have shown that our printing department will not be viable in its current form."
However, Ann Field, national officer at Unite, said that both parties are still in early talks and at present the union is talking "in terms of retaining jobs at Cambridge and not redundancy packages for workers".
"With the rally on Saturday (14 February), we hope to raise awareness locally and across the country about the virtual elimination of the Cambridge printing operation."
The University Press claimed that with 80% of its publishing sales located in countries outside the UK, it had experienced an increasing need to offer improved turnaround times and cheaper transport costs.
Cambridge University Press pledges "enhanced" redundancy deals for potential staff cuts
Cambridge University Press (CUP) has reiterated its intention to support the up to 150 staff affected by potential cuts at the company, claiming that those made redundant will receive "enhanced" redundancy packages.