The struggling midrange retailer wants to replace returning CEO Mike Ullman, the network said.
Ullman, CEO from 2004 to 2011, returned to the helm in April after Penney ousted CEO Ron Johnson, a former Apple Inc. executive, after 17 months on the job.
Several of Johnson's decisions, including a pricing-strategy change, were called into question after a customer backlash.
Johnson had helped build Apple's retail operations.
Another former Penney CEO, Allen Questrom, credited with turning around the company when he had the reins from 2000 to 2004, is being wooed to return as chairman, CNBC said.
Questrom told the network Thursday he would consider becoming chairman only if he could agree with the CEO choice and if the board wasn't "hostile."
The company has "such a great history, you wouldn't want to give up until it's dead," Questrom told CNBC.
He said there were not more than five people in the country qualified for the CEO job.
Penney's board agreed in July to start a search to replace Ullman, CNBC said, citing a letter to the board from hedge-fund manager Bill Ackman, one of the company's biggest investors.
Ackman said he was "very concerned" about the company's future and expressed frustration the search process was going too slowly. He said he wanted a new chief installed by next month.
"Considering the scale of J.C. Penney, the seriousness of the issues it faces and the complexity of its business, there are only a handful of executives with sufficient talent and experience to take on the CEO role," his letter said.
"I strongly urge that we immediately put together a short list of candidates, determine their interest level, and schedule a fast-track interview process with the board," the letter said.
The retailer had no immediate comment on the report.
Britney Spears on kissing Ryan Gosling, Justin Timberlake in the Mickey Mouse Club
Theater accidentally screens 'Nymphomaniac' trailer instead of Disney's 'Frozen'