(CNN) - Condoleezza Rice is hopeful that Jeb Bush runs for president in 2016 but said it's unlikely she'd be seen on a ballot with the potential candidate.
In an interview with Ozy Media, the former secretary of state also said more questions need to be answered about the deadly 2012 terrorist attack in Benghazi, though she argued the issue could be approached in a less partisan way.
'Jeb would be fantastic'
Rice has a long history with the Bush family. In addition to serving as national security adviser and the nation's top diplomat in the George W. Bush administration, she also worked for former President George H.W. Bush.
Rice said she thinks Jeb Bush, a former Florida governor, would be a "fantastic" candidate.
"Jeb hasn't said whether he will run. He's a friend. I hope he does, frankly," she told Ozy's Carlos Watson in the interview published Thursday.
In the constant ebb and flow of 2016 speculation, a Bush-Rice ticket has been floated as a potential GOP pairing. She was also mentioned in 2012 as potential vice presidential candidate.
But Rice, who runs the Hoover Institution at Stanford University in California and serves on a number of corporate boards, once again shot down the idea of running for office.
"It's just not in my DNA," she said.
But she acknowledged "there are several others who are considering (running for president) who would be outstanding."
Asked about her thoughts on Sen. Ted Cruz, Rice gave a diplomatic answer, saying she doesn't always agree with the freshman senator from Texas but recognized that not every Republican has to be "backed by the establishment."
"Somebody who goes through the process and gets elected, more power to them," she said, adding that Cruz's wife used to work for her in the National Security Council.
As for Sen. Marco Rubio of Florida, Rice also described him as "fantastic" and highlighted his background as a child of Cuban immigrants.
Rice stressed that she'll be looking for a candidate who favors immigration reform.
"What I love about the way that Marco Rubio talks about our country–or Jeb Bush for that matter–is that sense that 'We the people' is an inclusive concept," she said. "It's not 'those people out there' and 'we the people in here'."
Would she ever consider crossing the aisle backing another fellow secretary of state, Hillary Clinton?
"I have a lot of respect for her. It's a small club–the secretaries of state, or the 'living secretaries of state' as we call ourselves. A small, small club," she said. "I'm a committed Republican. I'll continue to fight for that party, and I'll fight for that nominee."
Benghazi shouldn't be 'political theater'
Clinton is seeing renewed criticism over the Benghazi attack as House Republicans form a select committee to investigate the assault that left four Americans dead, including the U.S. ambassador to Libya. Clinton was overseeing the state department at the time and has testified before Congress over security concerns leading up to the attack.
Rice agreed "there are still unanswered questions about Benghazi."
"They could be easily answered, but I think they need to be answered," she added. Rice said she's not interested in the debate over the now infamous talking points given to then-U.S. Ambassador to the United Nations Susan Rice.
More important, Condoleezza Rice argued, are questions about what happened during the attack and what the security situation was on the ground prior to the assault.
The issue has been repeatedly used as a major line of attack by Republicans against the Obama administration, with the focus on Clinton as she considers a presidential bid.
But Rice said the debate should be toned down.
"This can be handled...in a way that is open and isn't political theater," she said. "Done in the right way, with the right cooperation, we can put this to rest."