Policymakers say the East African nation suffers from a low national savings rate and analysts said Safaricom could be looking to target that untapped market with the new product, dubbed "Mali" (Kiswahili for wealth).
Mali, which will be capped at 70,000 shillings ($690) per saver, will offer an interest rate of 10% per year, higher than that offered by commercial banks, the Business Daily newspaper reported.
Safaricom confirmed it was testing a savings product called Mali, but did not comment on the other details in the newspaper report.
"If it comes on board, it will be a game changer to the ordinary Kenyan. It should do well for their returns," said Lisa Kimathi, an investment analyst at Standard Investment Bank.
M-Pesa, which allows users to send and receive cash, and pay for goods and services even on basic feature phones, has powered the company's earnings in recent years.
During the company's first half to the end of September, M-Pesa revenues grew by 18% to 41.97 billion shillings, with the number of users standing at 23.6 million.
Safaricom, part owned by Vodacom and Britain's Vodafone, already runs an overdraft facility on M-Pesa called Fuliza and it has savings services in conjunction with two banks - KCB Group and NCBA Group, which offer lower interest rates to depositors.
($1 = 101.5000 Kenyan shillings)
(Reporting by George Obulutsa; Editing by Duncan Miriri and Mark Potter)