Publisher Guardian News and Media (GNM) announced last week that it would planned to cut a quarter of the jobs at the east London facility.
However, Unite national office Steve Sibbald told PrintWeek that a decision has been made to ballot on industrial action against any compulsory redundancies.
Unite has to give GNM seven days notice ahead of any ballot, but Sibbald said that it could be turned around quickly, so a strike could be voted on within the next fortnight.
Sibbald said: "The problem we have at GNM is that the site has not been around very long, so the guys there only have four or five years' service.
"It is quite a young plant too; often if redundancies are offered in our older sites it is almost seen as an early retirement present, but to these guys the job is of far more value than the payment so they are very keen to protect the jobs."
A spokeswoman for GNM said: "We are still in consulation with staff about the proposed redundancies and any suggestion of industrial action seems somewhat premature at this stage.
"As we said at the outset, we very much hope to achieve the the reduction of 27 roles via voluntary redundancies and that remains our ambition."