Another day, another rumor over whether Caroline Kennedy will make a formal foray into politics.

Over the weekend, the news was that New York Gov. David Paterson talked to JFK’s daughter about the possibility of filling Sen. Hillary Clinton’s Senate seat next month. Today, the news is that Kennedy’s chances of being named by Paterson to the post are pretty slim — 20-1, in fact.

The New York Post reports that a source close to the governor is saying that although Sen. Ted Kennedy, Robert F. Kennedy Jr. and other members of the Kennedy clan are pushing for their kin to be the next senator from New York, they may want it more than she does.

"It looks to me like [Caroline’s cousin] Bobby Kennedy may be trying to push Caroline more than Caroline is pushing herself," a Paterson administration source told The Post.

“I believe that she is considering it,” RFK Jr. told The New York Times on Friday. “A lot of people the last couple of weeks have urged her to do it.”

He also told the AP she would be a great advocate in education: "I know she’s interested … She spent a lot of her life balancing public service with obligations to her family. Now her children are grown, and she is ready to move onto a bigger stage." 

Caroline Kennedy isn’t nearly as obsessed with politics as some others in her family. She prefers to work on her favorite issues — such as education — quietly on the side. To that end, the Post also says Paterson may be concerned that Kennedy doesn’t have the aggressive personality it takes to bring home the bacon for New York — particularly when the state is in such dire financial straits. But it has been reported that Paterson wants a woman or non-white candidate for the position.

"The bottom-line question is: Can Caroline Kennedy be the tough, hard, calculating, aggressive, articulate and, yes, obnoxious type of senator New York needs and expects?" said a second administration insider.

Barack Obama even weighed in — sort of.

"Caroline Kennedy has become one of my dearest friends and just a wonderful American, a wonderful person. But the last thing I want to do is get involved in New York politics," Obama said Sunday on MSNBC’s "Meet the Press."

It’s also doubtful Clinton would be pleased seeing her seat go to a Kennedy. After all, big Ted, the Lion of the Senate, turned on her and supported Barack Obama in the Democratic presidential primary race. That’s gotta still sting.

Speaking of Ted Kennedy, the Massachusetts Democrat — diagnosed with brain cancer this year — on Sunday stepped down as chairman of the Senate Judiciary Committee. He will keep his chairmanship of the Senate Health Committee to keep his focus on health-care reform, and plans to return to Congress in January.