It was unclear how much Skilling's sentence could be reduced if an agreement is negotiated.
The department posted a notification on its website to victims of the Enron fraud and bankruptcy that prosecutors may resentence Skilling, the Los Angeles Times reported Thursday.
In 2006, Skilling, who was Enron's president, was convicted on 19 counts that included insider trading, conspiracy and securities fraud. He has served six years in prison and his attorneys have tried several times to overturn his conviction.
"The Department of Justice is considering entering into a sentencing agreement with the defendant in this matter," the notice said. "Such a sentencing agreement could restrict the parties and the court from recommending, arguing for, or imposing certain sentences or conditions of confinement."
The notice said people believing they were victims and wanting to voice their opinion to the Justice Department "about entering into a sentencing agreement, and/or to the court about accepting such an agreement," have until April 17 to do so.
Any changes must be approved by Houston U.S. District Judge Sim Lake, who presided over the trial.
A federal appeals court in 2009 ruled the 24-year prison term Lake imposed was too severe but resentencing was delayed while Skilling's attorneys worked on a broader appeal.
Enron collapsed in 2001 in what was then the largest corporate bankruptcy. Thousands of workers lost their jobs and much of their life savings.
Skilling has maintained his innocence.
The Times said its requests for comment to his defense attorney, Daniel Petrocelli, were not returned
In 2010, the U.S. Supreme Court ruled a federal "honest services" law, used to help convict Skilling, was too broad and partly overturned his conviction.
Later, a federal appeals court said that, despite the Supreme Court ruling, the verdict would have been the same under the "beyond a reasonable doubt" measure, the Times said. The Supreme Court last year refused to hear Skilling's appeal of that court decision.
Celebrity Breakups and divorces of 2014 [PHOTOS]