A spokeswoman for Wipro, India's third-biggest software service exporter, said the company had no comment to make.
However, a source in the company who did not wish to be identified said that oil giant Shell was a customer.
"Yes, Shell is a customer, but I cannot give you more details," the source said, adding that there was no partnership with IBM.
Industry analysts say large outsourcing deals involve multi-year contracts, and the revenue is spread over a long period.
The newspaper said the contract would involve "some high-end information technology and back-office jobs to support accounting and marketing and processing departments."
It did not give other details.
In addition to its software business, New York-listed Wipro has a unit that specialises in call centre services.
IBM has a large services division with a significant presence in India.