Banking giant Lloyds TSB is considering outsourcing overseas, to places which could include India, South Africa and China.
The group said although it had no firm plans, it was looking at a range of options to increase efficiency which could include outsourcing abroad.
The comments came in reaction to a report which said the bank was planning to set up overseas centres which could threaten up to 8,000 UK jobs.
It said places under consideration were India, South Africa and China.
The report said Lloyds was weighing up plans to set up centres for some of its technology and administrative functions, and was thought to be considering transferring some work abroad for its Scottish Widows subsidiary.
Ian Partridge, general secretary of Lloyds TSB Group Union, was quoted as saying: "One option being considered is India.
"The exporting of jobs and livelihoods from the UK to India, or anywhere else, is something the union will oppose vigorously."
A spokeswoman for Lloyds could not say what functions the bank was considering outsourcing and could not comment on the impact on UK jobs.
She said: "We have got no firm plans to do this, we are talking about outsourcing.
"With a business the size of ours, we are always looking at a range of options.
"We are always looking at ways to increase efficiency. We look at so many things but we don't have any firm plans to do it.
"Outsourcing could be in the UK or overseas so I would imagine we would look at pretty much anywhere. It is one possibility."
She could not rule out outsourcing to countries such as India, South Africa or China.
Lloyds has 81,000 staff worldwide, of which about 70,000 are in the UK.
In February, it announced plans to cut its staff by 5,000 but create 2,000 jobs in sales and services.
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