Unite regional officer Martin Hodges said the vote took place on Sunday (24 January) and that the result was "overwhelmingly" in favour of a ballot.
Hodges said: "The ballot papers are with the legal department and they'll be going out within a fortnight."
Employees are unhappy that former owner Newsquest "unilaterally changed" the terms of employment.
Unite said that the new terms cut staff redundancy entitlement prior to the printer's sale to Wyndeham Press Group-owner Walstead Investments.
A spokeswoman for Wyndeham Press Group said this latest development merely confirmed that a ballot on strike action would take place.
Vote reaffirms strike threat at Southernprint
Industrial action at Southernprint looks increasingly likely after staff voted for a second time in favour of a ballot on industrial action.
