Mississippi Gov. Haley Barbour (R) hasn't said if he'll make a 2012 presidential bid but he does have one person he doesn't want to run: New York City Mayor Michael Bloomberg.

"I hope Mayor Bloomberg won't even consider that," Barbour told CNN. "But if there were a strong third-party candidate, there's no question in my mind that candidate would draw votes away from the Republican."

Bloomberg originally ran for NYC mayor as a Republican but changed his voter registration in 2007 and ran for reelection as an independent.

But Bloomberg said Tuesday he doubts an independent candidate could win the White House.

"Party affiliation is so strong that ... you could get every independent vote, (and) it would still not be a majority," he told a group of chief executives and policy-makers in Washington, according to Reuters.

Barbour told CNN a third-party bid by Bloomberg would be "the best thing that can happen to President Obama" because of the GOP votes Bloomberg could win.

Barbour wouldn't talk about any presidential ambitions on his part. He said: "It's not like I've got to decide by Christmas or I've got to decide by Valentines or I've got to decide by any day, but I am going to seriously think about it and come to a decision in the next few weeks or months."