The incentives range from cash-backs to reward points, similar to those offered by the banks on credit and debit cards, they said.
The sources declined to be named as they were not authorised to speak to the media. The RBI did not respond to an email seeking comment.
The RBI started a pilot program for the e-rupee in December and is targeting a million transactions daily by year-end. But retail transactions are still tracking below the target, averaging around 25,000 a day, prompting the central bank's push, the first of the three sources told Reuters.
The central bank also introduced new features, including linking the digital currency to India's popular real-time payments system, Unified Payment Interface (UPI), to attract users, Reuters reported last month.
HDFC Bank, India's largest private lender, has rolled out such offers to expand the scale of such transactions, said Parag Rao, country head for payments, liability products, consumer finance and marketing at the bank.
Rao did not identify the specific offers it is running.
Smaller private lenders Yes Bank and IDFC First Bank are offering reward points that can be encashed for travel bookings, mobile recharges and cashbacks via FastTag, a highway toll collection system, according to the second of the three sources.
Other banks, including ICICI Bank and Union Bank, are also expected to roll out similar incentives, according to two executives at the respective banks.
Such "time-bound promotional incentives," for the CBDC are part of Yes Bank's digital strategy, a spokesperson for the bank said in an emailed response.
Emails sent to the other banks were not answered.
The banks are funding the offers themselves, all three of the sources cited earlier said.
Globally, countries like Nigeria offer rewards like discounts on auto-rickshaw rides to spur adoption of their digital currency but with limited success.
The incentives are largely "short-term measures," that will help drive volumes up temporarily, a senior banker at a private lender said. Banks, however, won't keep offering such incentives for long unless there is a clear business proposition, this person added.
(Reporting by Jaspreet Kalra; Editing by Dhanya Ann Thoppil)
By Jaspreet Kalra