NEW YORK (CNNMoney.com) - New York Mayor Michael Bloomberg has asked Time Warner Chairman and CEO Richard Parsons about running for mayor in 2009, according to a published report, but the media conglomerate chief reportedly said he isn't interested.

Bloomberg, who entered politics from his own media conglomerate, financial news service Bloomberg L.P., is prohibited from seeking a third consecutive term. The New York Post reports that Bloomberg and members of his administration are starting to focus more on his potential successor.

Time Warner Chairman and CEO Richard Parsons.

The paper reports that Bloomberg raised the idea a couple of months ago when he was talking with Parsons about heading an anti-poverty commission for the city. But while Parsons accepted the anti-poverty post, he told Bloomberg he wasn't interested in being mayor, according to the Post.

Ed Adler, a spokesman for Time Warner, also denied Parsons has any interest in the mayor's office.

"Mr. Parsons is focused on running Time Warner, and he's not running for mayor," Adler told the Post.

Time Warner is the parent company of CNNMoney.com.

Parsons, who served as a senior White House aide under President Gerald Ford and as counsel for New York Gov. Nelson Rockefeller, has also had his name surface in other recent reports as a possible U.S. Treasury secretary.

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For a look at Parsons' pay as head of Time Warner, click here.