-LRB- CNN -RRB- -- Caroline Kennedy , the 51-year-old daughter of President John F. Kennedy , has indicated her interest in filling the New York Senate seat being vacated by secretary of state designee Hillary Clinton . Caroline Kennedy has her eyes on the New York Senate seat . `` I 've talked to Caroline Kennedy and she 's clearly interested , '' New York Sen. Chuck Schumer said at a news conference Monday afternoon . He indicated that 12 people were interested in the position . `` She 's interested in the position , '' New York Gov. David Paterson confirmed . But at the same time `` she realizes it 's not a campaign . '' Paterson , who will name Clinton 's successor , noted that Kennedy had indicated a desire to `` sit down and tell me what her qualifications are . '' The Rev. Al Sharpton also released a statement Monday indicating that he had received a call from Kennedy `` who expressed to me her interest in -LSB- Clinton 's -RSB- Senate seat . '' Kennedy 's interest in the seat could mean the continuation of a family legacy in the Senate that began 56 years ago with the election of her father as the then-junior senator from Massachusetts . Background : The Kennendys in Politics '' Her uncle Ted Kennedy has represented Massachusetts in the Senate since 1963 , and her uncle Robert Kennedy served as New York 's junior senator from 1965 until he was assassinated in 1968 . `` Remember , -LSB- Clinton 's -RSB- seat in the Senate was once held by Robert Kennedy , '' said Bill Schneider , CNN 's senior political analyst . '' -LSB- Caroline Kennedy 's -RSB- other uncle , Ted Kennedy , is ill right now . If Paterson appoints Caroline Kennedy to the Senate , it means there could be a Kennedy staying in the Senate for quite a long time . '' Watch Sen. Schumer on the possible candidates '' CNN reported earlier this month that Caroline Kennedy had called Paterson to discuss the possibility of taking the seat . Paterson has the power to appoint a replacement , who will then face a special election in 2010 to fill out Clinton 's term . Paterson confirmed to CNN last week that Kennedy had called and `` asked a few questions '' about the expected vacancy . One Democratic source close to the Kennedy family told CNN earlier this month Kennedy was `` interested to say the least '' in the Senate seat and had asked a tight circle of other family friends and political advisers for advice . Before this year , Kennedy generally limited her forays into the public sphere to nonpartisan activity , penning books on civil liberties and serving as the de facto guardian of her father 's legacy . But in January , she backed a political candidate for the first time , announcing her endorsement of Obama during the Democratic primary season with an op-ed in The New York Times that drew days of the kind of media attention she has spent her life avoiding . `` I have never had a president who inspired me the way people tell me that my father inspired them , '' she wrote . `` But for the first time , I believe I have found the man who could be that president -- not just for me , but for a new generation of Americans . '' `` Apparently , she has acquired a taste for politics , '' Schneider noted . `` She wants to be part of this new regime in America , clearly playing a key role in the Senate if she gets that appointment . '' Watch Bill Schneider 's report '' There are a slew of high-profile candidates for Clinton 's Senate seat , including New York Attorney General Andrew Cuomo , whose last name carries some star power of its own New York , where his father was once governor . Kennedy 's roots in New York also run deep . Her mother , Jacqueline Kennedy , relocated to New York after her husband 's assassination in 1963 , with children Caroline and John F. Kennedy Jr. . Caroline Kennedy has also spent most of her life in the city , working there after graduating from Harvard , meeting her husband , Edwin Schlossberg , on the job at the Metropolitan Museum of Art , and attending Columbia Law School there . Her most prominent public roles involved overseeing her father 's presidential library and presenting the annual Profiles in Courage Award . She 's also edited several books , from a volume of children 's poetry and an updated edition of her father 's book `` Profiles in Courage '' to a collection of patriotic verse -LRB- `` A Patriot 's Handbook : Songs , Poems , Stories , and Speeches Celebrating the Land We Love '' -RRB- . Most of her leadership positions have been based in the arts : serving as host of the annual nationally televised Kennedy Center Honors in Washington and serving as the honorary chairwoman of the American Ballet Theatre , as her mother did . In late spring and early summer she was mentioned as a possible vice-presidential candidate and more recently as a contender for secretary of education in an Obama Cabinet . But elected office would mark a major shift for Kennedy . In a 2002 Time magazine interview promoting the updated `` Profiles in Courage , '' Kennedy would not rule out the possibility of a run for public office . `` I do n't have any plans to do that right now , '' she said . `` I do n't plan ahead . My kids are young , and I 'm really happy to be able to be around . But I do care about issues , and I 'm interested in them . So I do n't see that now , but you know , I have a long life ahead of me . '' CNN 's John King , Kate Bolduan , Mark Preston and Alexander Mooney contributed to this report .