ESL Investments Inc., run by Sears Holdings Corp’s Chairman Eddie Lampert, has offered $4.6 billion to buy the bankrupt retailer. The offer would keep about 500 Sears stores to remain open, according to a letter from his hedge fund filed with the Securities and Exchange Commission on Thursday.

Sears faces a series of deadlines this month to find a buyer that would keep it in business as some of its creditors call for it to shut down, according to Reuters. Preliminary indications of interest for Sears assets were due Wednesday.