New Delhi, May 26 -- A long-standing impasse between India's largest stock exchange and the market regulator regarding the exchange's public listing appears to be nearing a resolution. The possibility of such a breakthrough has lifted investors' mood, and sent unlisted shares of the exchange soaring in the grey market.

According to two people aware of ongoing discussions, the National Stock Exchange (NSE) may receive a no-objection certificate (NoC) from the Securities and Exchange Board of India (Sebi) for its initial public offering (IPO) within weeks, potentially ending years of litigation and regulatory deadlocks.

Two options are being discussed, according to the two people cited above, who spoke on condition of anonymity. One: Sebi...