The former Alaska governor herself has dropped several hints that she might be considering the challenge.
She recently told ABC's Barbara Walters that she is seriously considering a run for the White House, and she believes she could beat President Obama in 2012.
"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.
When questioned by Walters, "If you ran for president, could you beat Barack Obama?"
Palin responded, "I believe so."
The feisty Fox News contributor, whose daughter Bristol this week placed third in Dancing with the Stars, also hasn't shied away from taking on the Republican establishment.
On Wednesday, she took on the Bushes after comments by former first lady Barbara Bush that she hopes Palin would stay in Alaska.
"I think the majority of Americans don't want to put up with the blue bloods -- and I say it with all due respect because I love the Bushes -- but the blue bloods who want to pick and choose their winners instead of allowing competition to pick and choose the winners," Palin said on Laura Ingraham's radio talk show.
While Palin remains a popular figure among Tea Partiers and conservatives, she has yet to gain widespread support, polls show and many Americans still view her as a polarizing figure.
A Quinnipiac poll of primary voters released this week shows Palin leading her possible Republican challengers Mitt Romney and Mike Huckabee by a slim margin. But when pitted against the president, Obama leads Palin by 48-40 percent, while Romney leads Obama by one percentage point.
In an ABC News/Washington Post poll conducted late October, two-thirds of Americans regarded Palin as unqualified to serve as president.
ABC News' Mary Bruce contributed to this report.