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The bank has yet to take a final decision on whether to go ahead with the contract, which could be worth £100m a year, but an agreement could be announced before Christmas. In August, Computer Weekly revealed that Barclays was in talks with a range of suppliers.
The deal would be one of the largest outsourcing contracts in the banking industry.
The application development division of Barclays IT department, called Build Services, employs 2,000 people and helps the bank harness new technology as well as being responsible for applications.
Earlier this year Barclays handed over the management of its 42,000 desktops to EDS in a deal valued at £214m.
Toby Broome, chief operating officer for IT and operations at Barclays, said, "Our approach is for selective outsourcing. We do not dogmatically outsource." He declined to comment on the nature of the possible deal with Accenture.
A growing number of companies are choosing to outsource their IT systems to a range of specialist suppliers rather than relying on a single supplier.
"With the size of outsourcing deals now, no single supplier can do everything," said Anthony Miller, research director at analyst firm Ovum Hollway. "The trend towards multi [supplier] outsourcing is inevitable."
To minimise the cost of managing separate outsourcing deals, Miller said users should nominate a prime contractor to take responsibility for delivering the service and liaise with other suppliers involved in the deal.
Keith Brookes, national secretary of Unifi, said the union was in discussions with Barclays management over the proposed deal with Accenture.
Brookes believes 1,700 jobs could be outsourced, with some jobs moving overseas if the deal goes ahead.
The union has called on the bank to avoid compulsory redundancies and retrain and redeploy IT staff if jobs are lost.
Accenture declined to comment