The three merchant bankers selected for the stake sale are J P Morgan, Citigroup Global Markets and JM Financial Consultants, sources said.
The share sale will take place through block trade, they added.
SUUTI, formed in 2003 is an offshoot of erstwhile UTI, holds 23.58 per cent in the country's third largest private sector lender Axis Bank.
The other promoters of the bank are Life Insurance Corporation, General Insurance Corporation, New India Assurance and National Insurance Company.
The stake sale of SUUTI in Axis Bank is part of disinvestment process.
The government has budgeted Rs 14,000 crore by way of residual stake sale in companies in which it does not hold a majority stake.
Earlier this month, the government decided not to wind up SUUTI for the time being, paving way for sale of its holdings in three private firms -- ITC, L&T and Axis Bank.
With the government deciding not to wind up SUUTI, it would be able to offload its holdings in these companies separately on the basis of suitable market valuations.
The Cabinet had in March 2012 cleared the proposal to wind up SUUTI and create National Asset Management Company (NAMC). The NAMC was in turn to take loan from banks leveraging its assets to buy government stakes in public sector companies.
The government last year, however, decided not to wind up SUUTI.