Sears Holdings Corp. (SHLD) Chairman Eddie Lampert has raised his bid for the bankrupt retailer to $5 billion according to a published report.

The move comes after the company turned down a roughly $4.4 billion bid from Lampert earlier this week, CNBC reported.

Under the new plan, Lampert would assume tax and other bills Sears has incurred since declaring bankruptcy in October.

If the company accepts Lampert's bid, his investment company, ESL, would be able to participate in an auction on Jan. 14 against other potential buyers who want to liquidate the once mighty retailer's remaining assets.

Lampert's plan would save the jobs of an estimated 50,000 of Sears' 68,000 employees.

Sears shares rose 0.004 cents to end at 39 cents Wednesday.