The 126-year-old company, which also owns the Kmart discount store brand, was initially preparing to enter into liquidation on Tuesday after failing to reach an agreement over a $4.4bn (£3.5bn) bid.
It gives Sears a chance to survive, which appeared to be slipping way heading into the hearing.
"ESL is the largest creditor of Sears, and their offer includes a credit bid of $1.8 billion of the debt they hold - that's something that might be problematic going forward", Sarah Foss, a legal analyst at Debtwire told CBS MoneyWatch in December. "A bankruptcy auction for Sears' assets is not due until January 14".
"If Lampert's deal doesn't pay enough cash to pay their fees, they would have concerns", said bankruptcy attorney Kenneth Rosen of Lowenstein Sandler, who represents smaller creditors. Transform Holdco, a new entity controlled by ESL, said in a letter to Sears' investment banker that it believes keeping the Hoffman Estates-based retailer in business is the best way to preserve jobs and recover money the retailer owes.
US Bankruptcy Judge Robert Drain in the Southern District of NY, who is presiding over the case, could decide to give Lampert more time to improve his bid, the Reuters sources said, adding that a bankruptcy auction for Sears' assets is not due until January 14.
About $17.9 million of the $120 million deposit is nonrefundable and will cover the cost of delaying the company's liquidation if ESL doesn't emerge as the winning bidder, Schrock said.
Even though no other bidders stepped forward, Sears Holdings' board decided the offer wasn't good enough since almost a quarter of it was in the form of debt forgiveness. A liquidation would likely shut hundreds of Sears and Kmart stores, potentially putting more than 50,000 people out of work.