The government aims to raise at least $2.5 billion by selling a 5 percent holding in the country's biggest oil producer through an auction on Thursday.
Traders said they expect heavy bidding in the auction and foreign fund inflows could top the target amount.
The rupee strengthened to as much as 48.83 to the dollar, a level last seen on February 7, according to Thomson Reuters data.
At 10:33 a.m. (0503 GMT), it was at 48.97/98, still 0.2 percent firmer than Tuesday's close of 49.0750/0850.
There is a bias towards dollar sales on account of the ONGC share issue, said a senior foreign exchange dealer at a state-run bank. If inflows remain strong, the rupee could strengthen past 48.80 and then see a move to 48.68.
Foreign funds have bought Indian shares and debt worth $11.74 billion so far in 2012, according to data from the Securities and Exchange Board of India.
The inflow has boosted the rupee 8.4 percent this year after it fell nearly 16 percent in 2011.
The benchmark share index rose more than 1.4 percent on Wednesday, with ONGC among the gainers.
Traders were also upbeat that the European Central Bank's planned cash injection later on Wednesday would boost global risk appetite.
New Delhi is set to release gross domestic product growth data for October-December around 0530 GMT, and economists expect growth at around 6.4 percent, the slowest in more than 2 years, a Reuters poll showed.
One-month offshore non-deliverable forward contracts were at 49.38.
In the currency futures market, the most-traded near-month dollar-rupee contracts on the National Stock Exchange, the MCX-SX and the United Stock Exchange were all around 49.39, on a total volume of $895 million.