Sears Holdings said Monday it has formed a special committee to independently review a proposal from CEO Eddie Lampert's hedge fund, ESL Investments, to buy some assets from the department store chain.

The company said it's initiating a "formal process" to explore the sale of the Kenmore brand, its Parts Direct business and portions of Sears' Home Improvement division.

Sears' stock was up about 6 percent Monday, trading around $3.60 a share, after jumping more than 14 percent on the news.

The company added that it's considering "other alternatives ... that may maximize value" for Sears.

In ESL's proposal sent to Sears last month, the hedge fund said it would also consider making a bid for some of the retailer's real estate assets. Sears has shuttered hundreds of stores over the years to raise cash to fund operations and put money into its pension plan.

Lampert has said his goal is to get Sears back to profitability by running an "asset light" business. The retailer's sales have been declining at a double-digit percentage for consecutive quarters.

Sears said Monday it won't comment further about any asset sales "until it determines that additional disclosure is appropriate." Lampert has said he won't take part in any discussions or decisions that involve ESL as a buyer.

Sears' special committee has retained Centerview Partners as its investment banker and Weil, Gotshal & Manges as legal counsel.

As of Friday's market close, Sears Holdings' shares were down about 65 percent from a year ago.