The company announced early Monday that the CEO will be stepping down, and John Flannery, current president and CEO of GE Healthcare, has been named chief executive of the company, effective Aug. 1.
"We've been long calling for an AT&T-style breakup of GE, and we would expect the new CEO to consider something down that path," Davis said.
Flannery comes with a heavy finance background, and analysts and investors are expecting him to complete a "quick and serious" review of GE's portfolio upon assuming his new role. Davis said he expects Flannery to ultimately break up many of GE's businesses.
"It's hard to imagine that you can see synergies between health care and power generation aircraft engines," he told CNBC, suggesting a potential spin-off of GE Healthcare could already be in the works.
"If you're a new CEO, and you come out of a portfolio review and don't do anything, that would be a statement," especially considering how unhappy shareholders are, Davis added.
"We're expecting fairly dramatic changes," he said.
As of Friday's close, shares of General Electric have fallen more than 11 percent for the year-to-date period. The stock was climbing a little more than 3 percent Monday morning on news of Immelt's departure.