[cnn-photo-caption image= http://i2.cdn.turner.com/cnn/2008/images/12/05/art.kennedy.gi.jpg caption="Caroline Kennedy's name is being talked about for Clinton's senate seat."]
(CNN) - Could Caroline Kennedy, considered to be among the most private members of the Kennedy clan, be tapped to fill Hillary Clinton's Senate seat?
Kennedy - who endorsed Barack Obama in February before the Super Tuesday round of primaries - is said to be considering the possibility, according to an ABC News report.
New York Gov. David Paterson, the man tasked with picking Hillary Clinton's successor, is remaining mum on the process, but a spokesman for Barack Obama issued a statement in the wake of rumors the president-elect is quietly lobbying Patterson to choose Kennedy.
"President-elect Obama has a very high regard for Caroline Kennedy," said Obama spokesman Stephanie Cutter. "But he has not spoken with Governor Paterson or Caroline Kennedy about the race, and has no involvement in this process."
Earlier, similar rumors circulated that former President Bill Clinton might be interested in the job, but the former president's office quickly released a statement saying he was not interested.
Caroline Kennedy's cousin, Robert F. Kennedy, Jr., was also discussed as a potential successor, but formally took his name out of the running earlier this week.
Paterson still has a strong bench to choose from. There are a number of contenders, including several members of New York's delegation in the House of Representatives, New York State Attorney General Andrew Cuomo, Buffalo Mayor Byron Brown, Bronx Borough President Adolfo Carrion, and Nassau County Executive Thomas Suozzi.
Whoever is chosen would have to be ready for virtually non-stop campaigning and fundraising over the next four years. Clinton's successor will face a hotly-contested campaign in 2010 to fill out the remainder of her term, then a re-election bid jut two years later.