Under the plan being considered only one bank branch would open every five kilometre (3 miles) in major cities, the sources, who declined to be identified as the talks about the closures have not been publicly disclosed, told Reuters.
"Banks are trying to see if they can only keep one branch open in a radius of 5 kilometres" C. H. Venkatachalam, general secretary, All India Bank Employees' Association (AIBEA) said.
AIBEA represents about half a million bank employees spread across several major government, private and foreign banks. HSBC has announced that some of its branches will not be in operation from Thursday until the end of the lockdown.
The Reserve Bank of India and the Indian Banks' Association did not immediately respond to requests for comment.
Most banks have already pared opening times to a few hours and are urging customers to use digital services in India, which has reported 649 coronavirus cases and 13 deaths.
A finance ministry official said 90% of banks and ATMs were working normally and he was not aware of any plan to shut them, adding that: "The government is monitoring the situation daily".
The official referred to an order issued by the federal interior ministry exempting personnel involved in banking operations, including IT firms supporting banking operations and cash management agencies, from the lockdown orders.
One of the sources said that under the plan banks in rural areas, where 70% of Indians live and are often completely dependent on cash, will likely operate on alternate days with staff focused on the disbursal of welfare money.
"The general guideline is that branch operation should largely be for villages just to take care of those people who are not familiar with digital transactions," a senior banker with a state-run bank told Reuters.
"Informally, banks are talking to each other to cope up with a situation where there will be some rush for cash withdrawal because it is expected the government will provide cash for the poor directly into their accounts," the senior banker added.
Some banks have already begun testing the planned approach in certain regions although it was not immediately clear when a full rollout would occur, two of the sources said.
In a bid to discourage account holders from visiting branches, the banking association has advised its 255 member banks to suspend non-essential services until further notice.
The plans have been under consideration for about a week, one source said, while another said senior central bank officials were on Wednesday checking how well prepared all banks were for digital banking.
Banks are also considering allowing inter-operable services, which would mean customers of one bank would be able to withdraw from any other bank and the transaction would be settled between the lenders, an official with a state-run bank said. ($1 = 75.3200 Indian rupees)
(Reporting by Neha Dasgupta and Nupur Anand; Additional reporting by Swati Bhat; Editing by Edwina Gibbs, William Maclean and Alexander Smith) ((firstname.lastname@example.org; +91-11-49548058; Reuters Messaging: email@example.com (Twitter: @neha_5))