Such a stoppage could lead to production losses of 840,000 tonnes, equivalent to around 381m (E560m).
The lockout would affect 24,000 members of the union, and would start on 18 May and finish on 1 June.
The threat follows weeks of stoppages, which have caused five days of production losses totalling 300,000 tonnes, estimated to have cost 136m.
FFIF communications manager Anne Kokkonen said that it had now reached serious levels, and that the lockout threat was the only option for the employers.
She said that deliveries by paper mills had been unaffected by the stoppages, due to their considerable stocks.
The unions have responded by announcing two-day strikes for pulp and paper workers, from 15 and 16 May respectively.
Story by Andy Scott
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