Shares of Sears Holdings Corp. on Tuesday jumped 6.4 percent on rumblings that the retailer could be close to selling its proprietary Craftsman tools brand for about $2 billion.

Sears said in May that it was taking a closer look at options for its three proprietary brands — Craftsman, DieHard automobile batteries and Kenmore kitchen appliances — to see what made sense, whether an outright sale, licensing or other distribution channels. The brands have long been considered the retailer’s crown jewels. In 2006, the company’s chairman Edward S. Lampert securitized the intellectual property assets of the three brands. Through the securitization, or $1.8 billion in notes backed by the intellectual property, ownership of the IP assets was moved to a separate entity called KCD IP. Licensing fees pay the interest on the notes.

The company at the time declined to discuss the possibility of a sale of the IP assets, although if one were to occur it could be a complicated transaction. The KCD entity is considered bankrupt remote, and KCD is listed as one of those assets that has a “ring-fence” in an agreement with the Pension Benefit Guaranty Corp., the government-run entity that insures pension plans. A Sears spokesman at the time said that any transaction would be completed in accordance with its existing contractual obligations, including the one with the PBGC.

Stanley Black & Decker and Hong Kong-based Techtronic Industries on Tuesday reportedly have made offers for the tool brand, while Apex Tool Group and Sweden-based Husqvarna AB were said to be mulling offers. Reports said that final offers are expected at the end of October, and that the offer price could be as high as $2 billion.

A sale would seem to underscore the dire financial picture at Sears Holdings. In August, when the company posted second-quarter results — the company said the loss for the period ended July 30 was $390 million, or $3.70 a diluted share, against profits of $208 million, or $1.82, a year ago — it said Lampert’s hedge fund, ESL Investment, agreed to give the retailer a $300 million bailout in the form of debt financing.

Sears has long maintained that it has levers to pull to finance its retail transformation. But time could be catching up — Fitch Ratings last week included Sears in its list of seven retailers with significant default risk within the next 12 to 24 months. The concern of the leveraged finance analysts at Fitch was over Sears’ ability to repay its $2.8 billion in high-yield bonds and institutional term loans.

And since the closing of about 60 Kmart stores in the past few weeks, there’s been market chatter that Sears also could be on the verge of shutting down the discounter. In a blog post Monday, Lampert sought to dispute those rumblings, noting that “there are no plans and there have never been any plans to close the Kmart format.” Lampert also went on the write that “Kmart continues to operate over 700 stores” and that a “significant number of these stores are profitable and have been profitable for years.”

Lampert also said in the blog, “We have a process underway to create value by positioning our Kenmore, Craftsman and DieHard businesses as well as our Sears Home Services business to benefit from broader distribution and partnerships that will allow them to grow beyond Sears Holdings. We also possess a significant portfolio of real estate assets with an opportunity to create value through improving our retail productivity and by monetizing them in a variety of ways.”

The shares closed at $12.10 in Nasdaq trading.