The deadline for talks has been put back to 30 April as the university and Unite continue to thrash out details of how many jobs could be saved at the historic site.
Cambridge University Press originally entered into a 90-day consultation with staff in January with a view to cutting around 130 positions.
However, in March it was revealed that nearly half of the 120 proposed print job cuts could be retained.
Since then, Unite has vowed to "press for more jobs" to be retained with national officer Ann Field claiming the union "won't rest until we have secured more employment".
She added: "If not, we want decent redundancy packages for those affected."
Peter Davison, corporate affairs director at CUP, told PrintWeek that while the consultation period with staff has been extended, it is unlikely any more jobs will be saved.
"The union chapel will be holding a meeting on 24 April in which it will outline our latest proposal to those affected," he said.
"We've discussed our offer, which includes slightly enhanced redundancy packages for the jobs that cannot be saved. In addition, we're investing in training for those made redundant."
Also see:
Unite seeks to save jobs at CUP