"I would like to see the very first woman in the White House who I agree with and who I think has policies that would really fulfill the goals that I have for our country," Clinton said during an interview on CNN's "American Morning" Tuesday.
"Of course, it's exciting to have a woman on the ticket," Clinton said of Alaska Gov. Sarah Palin being the Republican vice presidential candidate. "But that in and of itself is not enough reason."
She noted the Democrats nominated Geraldine Ferraro as their vice presidential candidate in 1984.
The glass ceiling won't be shattered until a woman is serving as president or vice president, said Clinton, who waged a historic run for the Democratic presidential nomination against the party's eventual standard-bearer Sen. Barack Obama of Illinois.
"But I am going to be supporting women and men with whom I agree," Clinton said, "who I believe have the right policies and the right ideas about what's best for America."
Celebrity Families of 2014 [PHOTOS]