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The contract with Hewlett-Packard will affect UK IT staff at the bank's Bristol and West operations and Dublin-based staff in systems and infrastructure services.
Members of the technology arm of the Irish Bank Officials' Association last month threatened strike action unless concerns over job security and staff consultation were addressed.
Larry Broderick, general secretary of the IBOA, said the organisation was still in discussions with the bank, but added that its members would take strike action if the Bank of Ireland attempts to force through the deal without reaching agreement with staff.
A spokeswoman for the Bank of Ireland said its staff consultation is likely to continue for up to six months before any deal is signed.