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In July, the council announced that it had shortlisted Atos KPMG, Cap Gemini Ernst & Young and a joint bid from IBM and ITNet for the 10-year deal, which is worth more than £100m.
The contract, which is due to be awarded in July, will support the Bradford-i project to overhaul the council's IT infrastructure.
Council IT staff voted to ballot for industrial action on 5 January to support their demands for secondment. The council's 135 IT staff are concerned that transfer to the private sector could affect their pensions and employment conditions.
Gurjit Singh, who chairs the Bradford branch of public sector union Unison, said, "When these people started working for the council, they chose to work for a public sector body, rather than the private sector, but now they are feeling threatened."
The council said it was holding "positive discussions" with unions on the issue.
Some local government IT staff have already been seconded to the private sector. About 750 workers, including 200 IT professionals, were seconded to BT as part of Liverpool City Council's joint venture deal with the telecoms giant, signed in 2001.