The Tatas own more than 60 per cent of Neotel, a provider of fixed-line service and data.
The talks are set to become exclusive, Bloomberg said. Neotel was not immediately available for comment and Vodacom declined to comment.
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"It is not our policy to comment on market speculation," a Tata Communications spokeswoman in Mumbai said. Reports of discussions to sell the firm have been swirling for most of this year and Vodacom's bigger rival, MTN, confirmed in August that it was no longer in talks for a stake in Neotel.
The Johannesburg-based carrier gained as much as 2 per cent to 128.46 rand ($12.75), the highest since January 4 on a closing basis, and was trading 0.5 per cent up at 126.64 rand at 10:05 am.
About 531,000 shares, or more than 25 percent of the three-month daily average, changed hands, according to data compiled by Bloomberg.