Feinstein, who didn't attend the Democratic convention in Denver because of a broken ankle, told the San Francisco Chronicle that she might choose to stay in Washington if Democrats gain a large enough majority in Congress to move major legislation.
"I can't say that since this (convention) started I haven't thought about it, because I have," Feinstein, 75, said Thursday of a possible run. "I want to see how close to 60 votes we can get in the Senate, what the committee structure is and how best I can use my time."
California's senior senator already chairs the Senate Rules Committee, but also has significant clout on the Intelligence, Appropriations and Judiciary committees.
"The job I do now I think is important, and what I really want to do is make a difference," Feinstein said. "The question is, how can I best do that? Is it using the seniority I have in the Senate, or is it in getting out there and running for governor?"
Feinstein said she sees no reason to rush into the decision to run in two years, when Gov. Arnold Schwarzenegger is termed out of office. The popular senator already has a campaign team, a large pool of donors and a network of supporters ready if she decides to run.
Other top Democrats considering a gubernatorial bid include San Francisco Mayor Gavin Newsom, Attorney General Jerry Brown, Lt. Gov. John Garamendi and Los Angeles Mayor Antonio Villaraigosa.
Feinstein, a former San Francisco mayor, was first elected to the Senate in a special election in 1992 and re-elected in 1994, 2000 and 2006. But she lost her first bid for governor in 1990 to Republican Pete Wilson.