They are due to meet with BAE Systems management on Wednesday to hear the outcome of two days of talks.
Last week the defence giant announced plans to cut 1,775 jobs at its sites in Scotland and southern England, where building would cease altogether.
However union officials say they have not yet given up hope of retaining some shipbuilding at the south coast yard.
Drop in demand
Discussions at BAE Systems' Farnborough headquarters between the union and bosses broke up earlier with neither side giving much away.
The results of the talks will be put to workers at mass meetings in Hampshire and on Clydeside on Thursday morning.
BAE – which employs 1,200 people in Portsmouth and 3,200 across its Govan, Scotstoun, Rosyth and Filton sites – has said it will end shipbuilding on the south coast in the second half of next year.
It plans to transfer the remaining work, on the Royal Navy's two Queen Elizabeth class aircraft carriers, to Govan and Scotstoun.
The move threatens 940 staff jobs at the Portsmouth yard and a further 835 in Glasgow, Rosyth and Filton in Bristol.
BAE says the cuts are necessary because of a “significant” fall off in demand.
Meanwhile, Minister for Cities Greg Clark has said parts of a regeneration deal signed between the government and Portsmouth were included because of the BAE job cuts.
The so-called “city deal” is aimed at boosting employment and development in the area.