Billionaire Lampert, who also runs hedge fund ESL Investments Inc, said the 125-year-old department store chain should take steps reduce its debt load to $1.2 billion from $5.6 billion. Lampert and his hedge fund, which he controls, own about 50 percent of Sears, according to Thomson Reuters data.
Lampert said Sears should offer creditors options to extend their debt or exchange it for new holdings, giving Sears more time to turn its business around.
Lampert said the company should continue selling real estate to reduce debt by $1.5 billion and that ESL would be a back-up bidder for the properties.
Sears said it has referred Lampert's proposal to a special committee.
In an internal message seen by Reuters, Sears said, "We will now be working aggressively to execute liability management transactions so that we can extend our runway and continue executing on our transformation strategy."
The proposals came as a Sears special committee weighs a prior offer from Lampert to acquire the retailer's Kenmore appliances brand and its home services business for as much as $480 million. Sears warned this month it could go out of business as it waits for approval from the committee on the deal.
The U.S. government agency overseeing the pensions of 100,000 of the company's former workers must also approve a sale of Kenmore.
Sears' shares, worth $30 in 2015, were down 3 percent at $1.24 Monday.
Credit ratings agency Fitch Ratings Inc said it viewed Lampert's proposed deal as "challenging to execute." Even if the deal is done, Sears would still need significant cash to operate because of challenges in retail, the ratings agency said.
In recent decades, Sears, which was the world's largest retailer in the 1960s, has struggled in the face of declining foot traffic at its brick-and-mortar stores.
In another attempt to avoid bankruptcy, money-losing Sears last year sold its Craftsman tool brand to power tool maker Stanley Black & Decker for $900 million.
(Reporting by Uday Sampath in Bengaluru, writing by Sweta Singh; editing by Steve Orlofsky and Cynthia Osterman)
By Jessica DiNapoli