The Maritime Union says mediation with the Ports of Auckland will resume on Tuesday afternoon and redundancies are on the agenda.
More than 300 union members have been taking industrial action over their collective contract.
The union says they have received a letter advising them redundancies will be discussed from 1.30pm.
It says it can not understand why the port company wants to discuss laying workers off, given that extra business has been created.
The union acknowledges the ports lost business when international shipping company Maersk moved one of its lines from Auckland to Tauranga a fortnight ago, but points out that another company, OOCL, has since announced increased use of the ports.
However, Ports of Auckland says that OOCL is not planning to make any extra ship calls to Auckland and Maersk's transfer has put it in serious financial difficulty.
The company's chief executive, Tony Gibson, says the reality is that redundancies are a possibility and that significant changes are needed if the port is to prosper.