Michelle Nunn is running on the Democratic ticket in an open race to replace Sen. Saxby Chambliss, a Republican, the New York Times reported.
Nunn said her father's name recognition has helped her political career in some ways.
"A lot of Georgians come up to me and say how much admiration they have for him," Nunn said. "No matter which way they're voting, they always consider themselves politically Sam Nunn Democrats. So it gets me a hearing for sure."
The former senator, who now runs an institute in Washington, D.C., devoted to eliminating nuclear weapons, said he initially had "mixed feelings" about his daughter's campaign, but watching his daughter discuss military policy at a breakfast she hosted for military industry and policy analysts changed his view of her race.
"That morning," he said, "was when I said to myself, 'Hey, she's got as good a shot as anybody in this race, maybe better.'"
Georgia Democrats also say they believe the younger Nunn has a shot at winning the race.
"It's a tough race, but she can win it," said Roy E. Barnes, Georgia's most recent Democratic governor, who lost a re-election bid in 2002.