The offer outlined Thursday included up to $950 million in cash through an asset-based loan facility, a "credit bid" of $1.8 billion and the assumption of roughly $1.1 billion in liabilities. The liabilities assumed include gift cards, points from its Shop Your Way loyalty program and protection agreements from Sears Home Services. Other funds include additional cash, notes and the rollover of cash collateral.

Sears Holdings, which owns Sears department stores and Kmart, filed for bankruptcy on Oct. 15. In previous court filings, it has said it was in talks with ESL about a "going concern bid" that could help the company emerge from bankruptcy.

The fund run by Sears Chairman Eddie Lampert, ESL Investments, submitted a $4.6 billion proposal on Thursday to help save the bankrupt retailer with the purchase of 500 stores.

Should the offer be approved, it would help about 50,000 of Sears' 68,000 employees retain their jobs, ESL said. The new company would reinstate the severance program it had in place prior to Sears' bankruptcy filing, ESL also said.

"ESL Investments continues to believe in Sears Holdings' immense potential to evolve and operate profitably as a going concern with a new capitalization and organizational structure," ESL wrote in the letter.

ESL may face other competition in its bid for Sears. A "stalking horse bidder" will be named on Dec. 15 in bankruptcy court. That bidder will set the floor for other potential offers. It could not be immediately determined whether others are looking to buy the company.

The offer itself will not ensure Sears' survival. ESL will need support from its creditors and approval from the bankruptcy court to proceed with its offer.

The company's unsecured creditors have already said they would prefer the company liquidate rather than sell to ESL, believing it is more valuable in pieces than as a company under ESL's ownership.

The use of existing debt to buy a company out of bankruptcy through a so-called credit bid is a controversial practice. Some view credit bids as giving investors who buy a distressed company's debt at cheap prices an unfair path to ownership.