Judge Robert Drain still needs to approve the agreement, but called the deal "a good development".
Plagued by falling sales and heavy debt, Sears filed for Chapter 11 bankruptcy reorganization in October and announced plans to close 142 of its roughly 700 remaining stores and eliminate thousands of jobs.
It gives Sears a chance to survive, which appeared to be slipping way heading into the hearing.
The company will pursue liquidation after it couldn't reach a deal with Chairman Edward Lampert on his $4.4 billion takeover bid for the 125-year-old chain.
A main point of contention in the negotiations between Lampert and Sears previously centered on whether Lampert's bid fully addressed the bankruptcy costs that Sears has racked up, according to sources familiar with the matter.
Lawyers for Lampert and his hedge fund, ESL Investments, were pressing for more time to sweeten his offer.
U.S. job gains seen picking up, may soothe jittery markets
Overall, healthcare employment increased by 346,000 jobs in 2018, up from 284,000 jobs in 2017, according to the bureau. That could mean the January jobs report released next month would show a drop rather than a gain in employment.
A hearing in the case is scheduled for Tuesday.
Lampert touted his merger of Kmart and Sears as laying the groundwork for their revival, a scenario that did not work out, and had the hedge fund manager relinquishing his role as CEO just after Sears filed for bankruptcy protection last fall.
Sears Holdings Corp agreed on Tuesday to consider a revised takeover bid from Chairman Edward Lampert, temporarily staving off a liquidation that would have spelled the end of the 126-year-old USA department store operator.
That bid had included $1.3bn (£1bn) in financing from three institutions, ESL said in a statement.
While current Sears shareholders have lost almost all their investment and creditors that include the US government are owed $11 billion, Lampert has pocketed nearly $1.4 billion to date from his investment in the retailer, calculated Institutional Investor in a recent story. Those creditors, which include Sears landlords and bondholders, have also questioned Lampert's pre-bankruptcy transactions with the retailer.
If Sears doesn't accept the $4.4 billion bid, Transform Holdco said it also would bid individually on some assets, including real estate, certain intellectual property and the Sears Home Services business.