Since chairman and CEO Eddie Lampert has done his darnedest to strip away everything of value from Sears Holdings (NASDAQ:SHLD), now might be the perfect time for him to get a buyer for his Kenmore appliance division.

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The name brand in appliances still ought to be worth a pretty penny. 

Reuters reported yesterday that Sweden's Electrolux (NASDAQOTH:ELUXY) may unveil a $2.5 billion offer for the appliance business from General Electric (NYSE:GE). It's no secret the latter was shopping the division and last month Electrolux confirmed it was interested in buying.

Many times one purchase in an industry spurs another, and since Sears' appliance business is causing a huge drag on the company's performance, it could be time for Lampert to strike while the iron's hot and shop the Kenmore brand to someone quick.

Kenmore used to be one of the the department store chain's crown jewels, owning a 40% share of the appliance market as recently as 2002. Through a special relationship it's had with Whirlpool (NYSE:WHR) in one form or another that dates as far back as 1916, it was Whirlpool that actually made the Kenmore appliances for Sears. Moreover, the agreement required Whirlpool to introduce features on the Kenmore brand first before it offered them on its own products.

Wash, rinse, repeat
Like much else that's been undone at the hands of Lampert, in 2009 Sears dissolved the pact with Whirlpool and instead partnered with LG Electronics and Samsung in a bid to save money. Kenmore's value cratered.

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Kenmore lost the cachet it once held for consumers after Sears CEO tried to wrangle more money out of it.

According to a Wall Street Journal story, features consumers looked for no longer appeared on the products and appliance sales are in a period of steady decline. Though Sears still leads the industry, its market share has fallen below 29%. Worse, the Kenmore brand has fallen from the top spot among appliances all the way down to third behind Whirlpool and General Electric.

In its second quarter earnings report Sears said that even though domestic comps sales at Sears rose 0.1% in part because of appliance sales, it wasn't nearly enough to offset the 1.7% drop in comps at Kmart, which was also a result of appliances, even though Kmart's hardline sales are about two and a half times smaller than Sears.

Sharply falling appliance sales in the division were also responsible for last year's near 4% drop in comps at both Sears and Kmart.

Before the value of Kenmore drops even more, maybe it's time for Lampert to get what he can.

New global reach
Analysts believe the price Electrolux is likely paying for GE's appliance business represents a high premium. 

GE's appliance and lighting division represented 5.7% of the conglomerate's total revenues of $146 billion and selling it to the Swedish company allows Electrolux a much bigger foothold in the U.S., where GE's business is almost exclusively focused. By partnering with an international company, it also gives the appliance division a chance to branch out globally.

Although Kenmore has slipped off its pedestal, it's still valuable. Sears hardlines segment accounted for 46% of its $8 billion revenues. Sure, that segment also includes things like consumer electronics, lawn and garden products, tools, hardware, and automotive parts, appliances remain a key component of it and the Kenmore brand specially so.

Foolish takeaway
Considering the long history Sears has had with Whirlpool, which might now be looking for an acquisition of its own to hold off a bigger, more robust Electrolux. 

For a number of years I've been critical of Lampert's reign at Sears Holdings, and lately continuous shedding of assets that's left the company a shell of its former self. But since he's doing so anyway regardless, now might be the best time for him to put Kenmore on the block and reap as much of a premium as he can, while he can.

Rich Duprey owns shares of General Electric Company. The Motley Fool owns shares of General Electric Company. Try any of our Foolish newsletter services free for 30 days. We Fools may not all hold the same opinions, but we all believe that considering a diverse range of insights makes us better investors. The Motley Fool has a disclosure policy.