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Government has chosen JPMorgan Chase & Co
The sale is part of a search for funds to narrow the government's fiscal deficit to 4.8% of gross domestic product in the financial year ending March 2014 from 4.9% a year earlier.
The government aims to raise around $9 billion by selling shares but has managed just 3% of that amount.
Half of its 20.7% stake in India's third-largest private-sector bank by assets is likely to be auctioned by the end of February, said the people, who declined to be identified as they were not authorised to speak to the media.
At the bank's current market price, the stake on offer is worth about Rs 5,700 crore, the people said.
A spokesman for Citigroup in Mumbai declined to comment, whereas JPMorgan and local brokerage JM Financial did not immediately respond to requests for comment. The spokesman at the finance ministry was not available for comment.
Slower-than-budgeted tax receipts and high public expenditure have increased the government's reliance on selling shares to narrow a budget shortfall in an economy growing at its slowest pace in a decade.
On Monday, the government approved the auction of its residual stake in Hindustan Zinc Ltd
The government, through the Special Undertaking of Unit Trust of India, also owns shares of cigarette maker ITC
The fiscal deficit by November had reached nearly 94% of the government's full-year target, piling pressure on the finance ministry to find alternative sources of revenue.
By fiscal-year end, it will receive a dividend of roughly $3 billion from state-run miner Coal India Ltd
