"Our going concern bid provides the best path forward for the company, the best option to save tens of thousands of jobs and is superior for all of Sears' stakeholders to the alternative of a complete liquidation, " the statement said.
Liquidation sales at the Kmart and Sears stores are expected to begin by mid-January, the company reported.
Sears Holdings filed for bankruptcy protection on October 15. Sears Auto Centers at those locations will also close.
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A hedge fund controlled by Lampert is the only entity to publicly disclose a plan to bid.
The latest nail in the coffin for Sears stores came Friday in an announcement that an additional 80 stores will close - including the WestShore Plaza location.
Lampert and ESL have been trying to buy the rest of Sears for up to $4.6 billion in cash and stock.
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According to reports by Reuters and CNBC, Eddie Lampert, the Sears chairman and its largest creditor, met a deadline late Friday imposed by the company for potential buyers of hundreds of stores and other Sears assets. As originally outlined, his plan would be partly funded by swapping the debt he holds for full ownership of the company.
Sears told the bankruptcy court it has interest from multiple parties.
The Sears at the Towne East Mall on East Kellogg is among 80 that will be closing nationwide in March. The Columbus store is not on the Sears Holdings list of those to be closed. Last week, US Bankruptcy Court Judge Robert Drain gave initial approval for the $60 million sale of Sears' home improvement business to Service.com.
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Sears announced Friday that it is closing 80 more stores, including the one on East North Street.