The company's scrip at the BSE around 2 p.m. jumped by 5.56 percent at Rs.611.80 per share from its previous close of Rs.579.60.
Talk of a possible stake sale has been doing the rounds for three months, ever since the government allowed foreign airlines to pick up 49 percent shares in domestic carriers.
In November, a government official said Indian private airlines were in touch with foreign carriers for sale of stakes.
"A possible stake sale is on the cards," said the official and added that talks were on with carriers based in the Middle East and Southeast Asia.
Reports of a possible stake sale also pushed the scrip of Jet Airways and it touched a 52-week high Dec 17.
The scrip at the BSE had recorded a 4.53 percent jump at Rs.636.70 per share from its previous close of Rs.609.10 Dec 14.
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Earlier, the government allowed foreign airlines to invest up to 49 percent in private domestic carriers.
The foreign carriers were so far not been allowed to directly invest in Indian carriers for security reasons although 49 percent FDI by non-airline players was allowed.
The Indian civil aviation sector has been going through a tough operating environment as high fuel and interest costs have hurt it.
The government expects that the decision will help bring in more funds to the airlines that have been cold-shouldered by banks.