NEW YORK (CNN/Money) - Reports that leading reality television producer Mark Burnett is interested in teaming with Martha Stewart on a new television show once she gets out of federal prison helped lift the battered shares of her media company.

Shares of Martha Stewart Living Omnimedia (MSO: Research, Estimates) rose nearly 5 percent in trading Monday, adding 58 cents to close at $13.17 after the New York Daily News reported that Burnett, creator of the successful "Survivor" and "The Apprentice" shows, is in talks with Stewart.

"I'm very interested in reinventing her show," he told the paper. He said the show would have nothing to do with her time in prison, and would have to do with her home decorating and cooking advice that was the core of her earlier show.

"The fundamental core will have to remain the same," he said. "It has to be about Martha helping people - cooking, lifestyles, that kind of thing."

Burnett is widely seen as the creator of the current reality television format that has become a major force in network television. His first major hit was the CBS show "Survivor," which debuted in 2000.

Among his shows is "The Apprentice," the hit show on NBC in which another famous business figure, Donald Trump, each week fires a different contestant who is attempting to win a job with his company.

Burnett describes himself as a friend of Stewart. His comments are virtually identical to an earlier interview he had with entertainment trade publication Daily Variety in May.

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The new report comes the week after Stewart announced she wished to start serving the five months in federal prison, to be followed by five months of house arrest. She was sentenced in July to the 10 months for obstruction of justice related to her sale of shares of ImClone Systems stock before damaging news about that company was made public.

Her announcement that she would start serving her sentence rather than waiting for an appeal to be ruled upon had already lifted shares of the stock. Shares are up nearly 15 percent since she announced she wished to start serving her time.

Still shares are down more than 20 percent since just before her conviction was announced March 5.

Viacom (VIA: Research, Estimates), which owns both the CBS and UPN networks, pulled Stewart's show "Martha Stewart Living" off its company-owned affiliates by in March in wake of her conviction. The show had been syndicated by Viacom unit King World.