Up to 200 IT jobs at the Department of Work and Pensions could be moved to India later this year by IT service provider HP.
The union that represents the workers, the Public and Commercial Services union, has not ruled out industrial action.
Department of Work and Pensions (DWP) operations in Newcastle, Lytham St Annes and Sheffield could be affected.
The Public and Commercial Services (PCS) union, which represents more than 2,000 members at Hewlett Packard in the UK, said the proposals are not yet approved and will go to the Cabinet Office.
But the PCS union warned that workers from Bangalore could be brought to the UK to gain the knowledge needed to do the jobs as early as August 2011. PCS said the jobs could be offshored as early as November 2011. PCS added that it had not ruled out industrial action.
The union says savings on IT would be overshadowed by the costs to the taxpayer through lost tax revenues and increased benefit payments to those losing their jobs. PCS said it is calling on the government to consider the wider economic arguments.
Mark Serwotka, general secretary at PCS, said: "The government must not allow low-paid jobs to be offshored. It will be a disaster for UK workers and the taxpayer and will only ensure that Hewlett Packard's shareholders reap the benefits."
In April last year HP averted a strike at the DWP with a pay settlement with workers.
Read this blog post for a series of articles by a UK IT professional who had to train the offshore workers that eventually replaced him.