Shares of the Estero, Fla., company-based were up 1.4% Wednesday to $3.00.
The two sides are still far from a deal, the Journal said, citing people familiar with the matter, which increases the likelihood that the company will file for bankruptcy court protection.
The restructuring is expected to trigger at least a partial liquidation of the Hertz rental-car fleet, the second largest in the U.S. behind Enterprise Holdings Inc.
The company initially asked holders of some of its $14 billion in asset-backed debt to accept an indefinite delay in payments, an offer they rejected, the Journal reported.
Hertz doesn’t own the cars, but rather essentially leases them from banks and bond funds that bought asset-backed bonds and loans used to purchase the vehicles.
The company has said that as a result of the pandemic Hertz and its subsidiaries have "experienced a rapid, sudden and dramatic negative impact on their businesses."
Last week Hertz said there is "substantial doubt" that it will be able to continue as a going concern due to the impact of the coronavirus outbreak.
Earlier this month, the company hired FTI Consulting to advise it on efforts to streamline operations in advance of a possible chapter 11 filing.
In another cost-cutting move, Hertz is reportedly selling off its fleet of Z06-based 2019 Corvettes, which the commissioned as a rental-car special for its 100th birthday in late 2018, according to Car and Driver.
On Monday, the rental-car giant said it had named Paul Stone as chief executive, succeeding Kathryn Marinello, who resigned.