The Economic Times business daily said that two Indian financial firms, ILandFS and IFCI, plan to sell to overseas investors part of their stakes in the bourse, the country's largest, "soon.
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The two lenders for large projects each hold a 7.1 percent stake. The newspaper said the exchange is valued at more than two billion dollars.
The National Stock Exchange was unavailable for comment.
The report follows a decision by the Reserve Bank of India to cap overseas investment in stock exchanges at 49 percent with direct ownership limited to 26 percent and funds that invest through listed shares at 23 percent.
The rival Bombay Stock Exchange (BSE) in Mumbai, Asia's oldest exchange, has also been approached by overseas investors, according to reports.
Singapore Exchange (SGX) said Tuesday it was in "preliminary discussions" with India's Bombay Stock Exchange to explore possible working opportunities.
On Tuesday, the Singapore Exchange, or SGX, said it was in "preliminary discussi