The firms asked include miner Coal India, power utility NTPC, minerals producer NMDC and Engineers India Ltd, said one of the sources, who sought anonymity as the discussions are private.
"Buyback is an important tool in our strategy and it helps in building market price," added the second official, who also spoke on condition of anonymity.
India is unlikely to be anywhere near its fiscal deficit target of 3.5% of GDP for 2020/21 as coronavirus curbs hit tax collections and delayed efforts to privatise energy firm Bharat Petroleum Corp and flag carrier Air India.
In February, the government had set itself a target of raising more than $27 billion from privatisations and sale of minority stakes in state-owned companies this fiscal year.
However, some companies, particularly in the oil sector, may not be able to do buybacks, the sources warned, as the government's stake is just sufficient to ensure its position as a majority holder.
"The government stake in these companies is about 51% and there is a competing claim on their cash in the form of huge capex commitment and dividend payments," the second source said.
But for those with sufficient funds and capital expenditure below target for this fiscal year, the government could seek approval from the cabinet to prune its stake to less than 51% in individual firms without giving up control, the official said.
India had tasked 23 state-run companies with capital expenditure of 1.65 trillion rupees ($22.5 billion) this fiscal year, but some firms face spending challenges as the world's second most populous nation adds virus infections.
The government had asked state-run firms to either meet their targets for capital expenditure or "reward the shareholder in the form of a dividend," the officials added.
(Reporting by Aftab Ahmed and Nidhi Verma; Editing by Clarence Fernandez)
By Aftab Ahmed and Nidhi Verma