Cain: Kissinger turned down offer to be secretary of State

It was unclear whether Cain was joking — reporters in the room laughed after the statement — but Cain met with Kissinger earlier this month in New York City to discuss foreign policy. After that event, Cain's campaign manager, Mark Block, told the National Review that Kissinger had described a Web ad in which Block smokes a cigarette as "brilliant."

"Halfway through Mr. Cain's conversation, Doctor Kissinger turns and points to me and says, 'That smoking thing you did was brilliant.' I sat there thinking, Dr. Henry Kissinger just said something I did was brilliant," Block said. "We all got a good chuckle."

Kissinger ranks among the most influential — and controversial — figures in American foreign policy. A recipient of the Nobel Peace Prize, Kissinger helped negotiate America's withdrawal from Vietnam and was a hugely influential voice on American relations with the Soviet Union.

Cain listed a number of other conservative icons as potential Cabinet members, including House Budget Committee Chairman Paul Ryan (R-Wis.). Cain said he "wholeheartedly" supported Ryan's plan for Medicare vouchers to replace the current benefit system.

"I support it wholeheartedly, which is why I have so much respect for him. He put something on the table that was going to solve the problem, knowing it was going to be controversial," Cain said.

The former Godfather's Pizza CEO also named Sen. Jim DeMint (R-S.C.), former Ambassador John Bolton, Fox News analyst KT McFarland and John Chain, former head of Strategic Air Command as potential fits for his Cabinet if he were to win the presidency. But, Cain said, the majority of the advisers in a hypothetical Cain administration would be from the business community.

"My administration will have a majority of businesspeople along with some seasoned officeholders who will not be afraid to challenge the status quo," Cain said.