Harris has served as district attorney in San Francisco since 2004.
Current Attorney General Jerry Brown is considered one of several possible contenders for governor of California in 2010.
A new Field Poll shows Brown has the early support of nearly a third of California democratic voters if he does decide to run.
The poll found that Democratic U.S. Sen. Dianne Feinstein had the highest favorable rating among the six Democrats and three Republicans listed as potential candidates.
Brown was next.
San Francisco Mayor Gavin Newsom had the highest unfavorable rating of all the potential candidates -- 41 percent.
The poll was conducted shortly before the Nov. 4 election, when voters rejected same-sex marriage, an issue that has defined Newsom.
The Field Poll of 527 registered voters was conducted Oct. 18-28 and has a margin of sampling error of plus or minus 4.5 percentage points.
Only one candidate -- Democratic Lt. Gov. John Garamendi -- has officially declared his candidacy for the 2010 race. Two others, Newsom and Poizner, have formed exploratory committees.
Feinstein has not said whether she will run for governor, particularly now that she is in line to become the first woman to lead the Senate Intelligence Committee.
She is popular among 70 percent of Democrats. That's greater than Brown, who was viewed favorably by 46 percent of Democrats but just 34 percent of all voters surveyed.
Popularity among members of their own party is important at this stage because candidates first must survive the primary election.
Despite his high unfavorable rating among all registered voters, Newsom had the third highest favorable rating among Democrats-- 38 percent. He was followed by Los Angeles Mayor Antonio Villaraigosa, who was viewed positively by 36 percent of Democrats; Garamendi, at 30 percent; and state Superintendent of Public Instruction Jack O'Connell, at 14 percent.
Newsom also had the lowest favorable rating among Republicans -- just 7 percent.