Amicus union is to press EDS to sign an agreement guaranteeing terms and conditions for its IT staff affected by offshore outsourcing deals.
Peter Skyte, national officer of Amicus union, said it would call for employees at the IT services provider to be given adequate consultation over offshore deals, guarantees over job security, redeployment and training.
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"We want employers like EDS to enter into agreements with us in order that the future skills and careers of the UK workforce can be safeguarded," he said.
A spokesman for EDS said it had begun discussions with EDS about a range of issues, including offshore outsourcing.
"We will continue to engage with Amicus on issues that are relevant to them and EDS, just as we would with any relevant trade union," he said.
Last month EDS said was to lay off between 15,000 and 20,000 employees over the next two years as part of an effort to cut £3bn (£1.7bn) in costs.
Outsourcing experts said the deal proposed by Amicus illustrates the hidden cost of offshore outsourcing and added that other outsourcing suppliers were likely to come under pressure to provide similar guarantees for IT staff who transfer to them from user companies, as well as their own staff.
Earlier this year Barclays and HSBC banks struck deals with banking union Unifi guaranteeing terms and conditions for IT staff affected by offshore deals.
Suppliers need to meet union concerns with agreements over offshore outsourcing just as companies such as Barclays have done," said Alex Blues, director at outsourcing advisory firm Orbys Consulting.
Phil Codling, a senior analyst at Ovum said any agreements over offshore outsourcing between suppliers and unions would not act as a barrier to offshore deals. He added that mounting pressure from unions over offshore outsourcing showed the extra costs companies face when trying to agree, particularly in the time taken in negotiation.