It is also the operation most dependent on the whims of U.S. consumers, who have been pinched by falling home prices and rising fuel costs.
Over the past few years, GE has sold off businesses accounting for more than $50 billion in revenue to try to grow faster, and after a stunning first-quarter profit slide, it has said it will look for other ways to reduce volatility.
Most recently, it announced plans to stop offering most loans for consumer boats and recreational vehicles.
Media reports said GE had hired investment bank Goldman Sachs Group to auction the appliance unit, which could raise $5 billion to $8 billion.
A GE spokesman declined to comment Thursday.
"This is probably a smart move," said Peter Klein, senior portfolio manager at Cleveland-based Fifth Third Asset Management. "It has not been an area where they have been able to bring a lot of ingenuity lately," said Klein, whose company oversees about $20 billion in investments and holds GE shares. That's been coming from the folks like LG and Whirlpool."
GE trails No. 1 U.S. appliance maker Whirlpool Corp and faces growing competition from Asian rivals such as South Korea's LG Electronics and China's Haier Group.
With the United States more than two years into its worst housing slump in decades and commercial credit markets still shaky, investors say this is a hard time to sell a home appliance business.
But the dollar's slide could make the unit appealing to an Asian rival interested in buying a well-known U.S. brand. At the same time, the brand itself is one of the risks GE faces in any sale.
While the company makes far more money on jet engines and commercial lending than it does by selling dishwashers, appliances are among its best-known products among U.S. consumers.
A drop in quality could tarnish GE's name even if it no longer made the devices, investors said.
In fact, the company was somewhat hesitant to sell its consumer product operations in the past "because whoever that buyer is going to be is going to want the GE brand name to go with it," said Peter Sorrentino, senior vice president and portfolio manager at Huntington Asset Advisors of Cincinnati.
GE shares are down about 12 percent this year after sustaining their worst drop in two decades on April 11, when the Fairfield, Connecticut-based company said quarterly profit fell 6 percent and warned full-year earnings could be flat.
The financial arms were responsible for much of the earnings decline, and GE executives said they would look for ways to reduce those units' volatility.
GE has already placed its U.S. private-label credit card and Japanese consumer lending businesses up for sale.
Some Wall Street analysts called for the company to think about selling off more of its finance units in the wake of the miss.
There has also been speculation that GE would sell its 80 percent stake in NBC Universal, which includes CNBC, but Chief Executive Jeff Immelt has repeatedly dismissed such talk. France's Vivendi SA holds the remaining 20 percent of the media operation.
Selling the appliance business had not been a major focus for Wall Street.
"This is a little out of left field in the cosmic scheme of GE," said Sorrentino of Huntington Asset Advisors, which manages $6.5 billion and holds GE shares. "This isn't a big area of focus that people were looking at, like NBC Universal. It has that feel that they're squeezing nickels and dimes out here and there now, as opposed to some bold master stroke."
Lehman Brothers analyst Robert Cornell wrote in a note to clients on Thursday that the company would do well to divest its GE Money consumer finance businesses and the rest of its consumer and industrial arm, which makes light bulbs and other products as well as appliances.
But he cut his 2009 profit forecast for GE, noting that "such an evolution could take many years, all the while distracting from what we expect to be very strong growth from the core."