Morgan Stanley co-presidents Ted Pick and Andy Saperstein, and head of investment management Dan Simkowitz, are widely seen as contenders for the top job.
Morgan Stanley shares were little changed in early trading, down 0.9%.
The less volatile business of wealth management accounted for 45% of firm's revenue in the first quarter.
Morgan Stanley's first-quarter profit beat expectations as rising revenue from wealth management offset declines in investment banking and trading.
Simkowitz, the eldest of the three at 58, is head of investment management at Morgan Stanley and co-head of the firm's strategy and execution.