Wealth management platforms are usually sold for about 2 to 3 percent of the assets under management, although the sources said it was not yet clear what price tag the unit could fetch.
Morgan Stanley has launched a strategic review of the division, the sources said, a process that typically ends with a sale.
The review is part of the bank's efforts to withdraw from subscale wealth management operations globally, one of the sources said.
The sources declined to be named because the sale process is not public.
A Morgan Stanley spokesman declined to comment.
The bank's India unit sale underscores a growing trend of consolidation in Asia's wealth management industry as private banks struggle to earn profits due to rising regulatory costs and wafer-thin advisory fees.
India is a particularly difficult market for wealth managers as cut-throat competition, high staff costs, weak markets and limited product offerings have squeezed fee revenue.
Many foreign players had scrambled to open up shop in India a few years back to take advantage of robust economic growth, only to find themselves struggling.
"Wealth managers have been trapped by the good potential macro of India," a top executive at a rival private bank familiar with the matter said.
India's ranks of millionaires shrank 18 percent to 125,500 last year, according to Capgemini and RBC Wealth Management's world wealth report released in June, reflecting a one-third decline in stock market values and a weakening rupee.
Last year was the first time India's wealthy declined in number since 2008.
But in the longer term, wealth is expected to rise steadily in Asia, with relatively brisk economic growth creating large numbers of new millionaires annually in India, China and across the region - a trend that banks have tried to harness to their advantage.
The challenge for the industry is that newly minted millionaires in Asia, rather than turning to private banks for help in preserving wealth as would clients in the United States and Europe, have treated banks more like brokers, working with several at once to increase their wealth.
Morgan Stanley Chief Executive James Gorman told an earnings call in July that scale was important in the wealth business for driving returns and that the bank was "taking steps to unlock value in our wealth management businesses outside North America".
The shakeup in the industry in Asia has accelerated since last year. Significant deals include Bank of America Merrill Lynch selling its overseas wealth management business to Julius Baer and HSBC selling its private bank in Japan to Credit Suisse.
Morgan Stanley launched its private bank in India with significant fan-fare in late 2008 as it marked the U.S. bank's first onshore wealth business in Asia. It was also planning to launch a similar business in China, but has yet to do so.
The India unit has 70 people on staff, the sources added.
The sale plan does not affect Morgan Stanley's other businesses in India, one of the sources said.
Les Menkes, who oversaw the launch of the India business, left the bank last year, separate sources familiar with the matter said.