"We are in discussions with them, but can't comment on the commercial terms of the deal," said a company spokeswoman.
Barclaycard, a unit of Barclays PLC's global and retail banking division, also confirmed the talks, on its website.
Firstsource's talks with Barclaycard come as Indian technology companies recover from the impact of the global economic slowdown, which led many of their customers to scrap or delay projects and seek lower rates for products and services.
The talks also follow an increasing trend of companies in the United States and Europe awarding outsourcing deals to Indian firms while asking them to take over their own low-cost centers, in India or other countries.
Analysts said a deal could be a significant boost for Firstsource.
"These kind of deals usually entail an up-front payment" by the outsourcing provider, but Firstsource would likely receive "a long-term outsourcing order" from Barclaycard, said Harit Shah, an analyst at Karvy Stock Broking.
