No financial details of the deal were disclosed.
"Firstsource Solutions Ltd... Has signed definitive agreements to sell a portion of its India domestic business, to Vertex Customer Management India," the BPO firm said in a regulatory filing.
It added that the sale is subject to approvals.
The company did not specify details on the reason for the sale and the contours of the deal.
Firstsource, which is part of the RP-Sanjiv Goenka group, had reported revenues of Rs 892.3 crore for the quarter ended March 2017. For the year ended March 2017, the revenues were at Rs 3,555.6 crore, up 10.5 per cent over the previous year.
Shares of Firstsource closed marginally lower at Rs 34.95 apiece on the BSE.