With an auction of its assets underway, the chairman of Sears Holdings has revised his offer to purchase a shrunken version of the once iconic retailer, a news report says.

Eddie Lampert, whose hedge fund ESL Investments offered more than $5 billion last week to buy nearly 500 Sears stores and properties, added more cash to his bid Tuesday to appease the company's creditors, according to Bloomberg which cited people familiar with the matter.

The latest twist in the discussions of Sears' fate occurred a day after an auction of the company's assets began. Sears Holdings declined to comment, and a representative of ESL could not be immediately reached Tuesday evening.

Lampert has loaned Sears billions of dollars in recent years to keep it afloat, and last week, his ESL Investments made a last-minute bid to salvage the company once again, upping an earlier $4.4-billion offer to over $5 billion to buy 425 stores along with 57 additional properties and inventory.

Sears, which also owns Kmart and has shuttered hundreds of stores amid listing sales, may have been immediately pushed into liquidation if ESL had not come forward with the offer.

The retailer, whose ubiquitous stores, wide array of offerings and iconic catalog made it a fixture in American life, has struggled in recent years to compete with more nimble and fashionable peers as well as online giant Amazon. The company filed for Chapter 11 bankruptcy protection in October.

ESL has said that it made a required $120-million deposit as part of its bid last week. Almost $18 million of it would not be refundable.

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