"I'm looking at the lay of the land now, and ... trying to figure that out, if it's a good thing for the country, for the discourse, for my family, if it's a good thing," Palin said in an interview scheduled to air in full Dec. 9 on ABC as part of Walters' "10 Most Fascinating People" of 2010.
Asked Walters: "If you ran for president, could you beat Barack Obama?"
Replied Palin: "I believe so."
This is the second time this week that the 2008 vice presidential nominee has shown that she is considering a run for the presidency.
In a New York Times Sunday Magazine interview, Palin told reporter Robert Draper that she is "engaged in the internal deliberations candidly, and having that discussion with my family, because my family is the most important consideration here."
Palin acknowledged that she'd have a tough fight proving her record to voters.
"I know that a hurdle I would have to cross, that some other potential candidates wouldn't have to cross right out of the chute, is proving my record," Palin told Draper. "That's the most frustrating thing for me -- the warped and perverted description of my record and what I've accomplished over the last two decades."
The Palin family has been in the spotlight this week with two television shows: "Sarah Palin's Alaska" premiered on TLC, and Bristol Palin made a surprise move into the finals of "Dancing With the Stars" on ABC.
While the Palin family has a strong group of supporters among conservative Republicans, a recent Gallup Poll found that 52 percent of Americans viewed Palin unfavorably. That's the highest percentage holding a negative opinion of her since the 2008 campaign.
Our question to you today: Could Sarah Palin beat President Obama in 2012?
ABC News' Mary Bruce and The Associated Press contributed to this report.