Fleming may be on the short list of the Manhattan-based brokerage firm, which is about to kick off a hunt for a new CEO after giving the heave-ho Thursday to Steven Freiberg.
Freiberg was two years into a four-year contract - over which time shares in the company have fallen about 48%.
The trading firm appointed Chairman Frank Petrilli to run the firm on an interim basis - making him the fourth leader in five years - until a new CEO is identified.
Fleming, sources tell The Post, would be a logical fit for running the online brokerage platform that has struggled to right itself since stumbling on toxic mortgages during the housing crash.
In the meantime, The Wall Street Journal reports that, in a bid to rejuvenate its ailing fixed income business, Morgan Stanley is 'scrambling to replace some of its well-paid bond traders with computers'.
The move to increase reliance on technology is already said to have accounted for between 10 - 20% of staff on some of Morgan Stanley's FX and interest-rate desks.
The newspaper reports that Glenn Hadden, the firm's head of global rates trading, 'has told colleagues the trading floor of the future will surround a few traders with the hum of powerful machines'.
Staff, it seems, will be Terminated.
image: © Ewen Roberts