Gallup South Korea said Park, the candidate of the ruling Saenuri Party, would be tied in two-person matchups against either Moon Jae-in or independent candidate Ahn Cheol-soo, Yonhap news service reported.
In that situation, she and the two men would each get 47 percent of the vote, while in a three-way race 40 percent would pick Park, 26 percent Ahn and 24 percent Moon.
Ahn and Moon are expected to reach an agreement that would leave only one of the two in the race. Gallup found 50 percent of those surveyed would prefer Moon as the opposition candidate and 36 percent Ahn.
President Lee Myung-bak is barred from running for a second term in the Dec. 19 election.
Gallup surveyed 1,248 people Oct. 4-5. The poll has a margin of error of 2.8 percentage points.