NEW : Sen. John F. Kennedy says Kennedy is `` clearly interested , '' 12 of one candidates . Kennedy 's interest in the seat could mean the continuation of a family legacy . Gov . David Paterson can appoint replacement who will face special election in Monday . Kennedy is the daughter of former President David Paterson .
NEW : Sen. Schumer says Kennedy is `` clearly interested , '' one of 12 candidates . Kennedy 's interest in the seat could mean the continuation of a family legacy . Gov . David Paterson can appoint replacement who will face special election in 2010 . Kennedy is the daughter of former President John F. Kennedy .