But the mayor also may bypass a third term. He even has a possible heir apparent in mind. And if that person runs, Anderson said he would be less likely to.
Even more surprising is Anderson's pick: Former City Councilman Keith Christensen, a Republican whose views on some high-profile issues have clashed with the liberal mayor.
"The person that I would love to see run for mayor if I don't - and if he would run I'd be more likely not to run - is Keith Christensen," Anderson told The Salt Lake Tribune.
The mayor apparently was more certain with Christensen. Over dinner at Al Forno a couple of weeks ago, "he said he would not run if I would make a commitment to do so," Christensen said Thursday in a phone interview from Catalina Island, Calif.
Christensen, who said he won't run if Anderson does, is seriously considering the mayor's suggestion. On Thursday, he wanted to know his potential opponents and his comments ranged from praising Anderson to trumpeting his own leadership style.
"I might have a little bit more public service left in me," said the 54-year-old Christensen, who served two four-year terms on the City Council through 2001 and sits on the city's airport board. "It's a major commitment. I don't take something like this lightly."
Christensen worked on Anderson's re-election campaign in 2003 and was touted as one of the mayor's GOP and LDS backers. He was one of 20 church members who signed a campaign advertisement defending Anderson against charges the mayor was "anti-Mormon."
As a councilman, Christensen voted to sell Main Street between South Temple and North Temple to the LDS Church. In 1997, he was on the losing side of the council when he voted against a nondiscrimination policy that protected gay city employees, and he later helped repeal that ordinance. Because of the council's flip-flop, Anderson signed a nondiscrimination executive order when he entered office in 2000.
But Christensen sometimes defied the council's conservative majority. He supported alcohol sales at Washington Square and the medals plaza during the 2002 Winter Olympics. He tried to change Pioneer Park into Pioneer Square to allow surrounding restaurants to sell liquor, but was rebuffed when the LDS Church opposed the plan.
Christensen and Anderson joined forces against a proposed outlet mall at 5600 West. The councilman sided with the mayor's suggestion to extend dance-hall hours. But he also told Anderson he was "dead wrong" for wanting to end the ban on State Street cruising.
While Anderson acknowledges he and Christensen have disagreed on some issues, the mayor said the former councilman fits his requirements for a successor, and he lauded his intelligence and leadership ability.
As Anderson decides whether he will chase re-election, he's thinking about who will protect what he sees as his legacy, particularly his environmental initiatives and youth programs. He wants someone who is "progressive" as well as someone who won't "go along to get along."
"I don't want to see somebody come in and destroy the progress we've been able to achieve," the mayor said. "It takes a lot of stamina and commitment as well as a lot of orneriness to keep pushing for progressive change against a council that is so resistant."
Christensen said the next mayor should build on Anderson's accomplishments. "Would I do things differently? Anyone would. Would I dismantle Rocky's initiatives? No."
Defying conventional wisdom, Anderson believes the Republican can win. The city race is officially nonpartisan, but party plays a role and a majority of capital residents are Democrats. And Christensen already is distancing himself from the GOP label, saying he is not an "extremist" and that "the management of Salt Lake City is simply not about partisan politics."
Salt Lake City voters haven't elected a Republican mayor since the mid-1970s. And even Anderson accused his 2003 Democratic opponent, Frank Pignanelli, of being too cozy with the GOP. Not even Gov. Jon Huntsman Jr., who lost in Salt Lake County, believes his party can win the capital. "I'm not sure a Republican can ever get elected in Salt Lake City," Huntsman said earlier this month.
Quin Monson, assistant director of BYU's Center for the Study of Elections and Democracy, said an Anderson-backed Republican would stand a greater chance of success. But Anderson's controversial reputation could taint any heir apparent's bid, Monson said. That happened in 1999, when Anderson crushed former Mayor Deedee Corradini's handpicked successor.
Democrats might be unhappy if Anderson endorsed a Republican, said Todd Taylor, executive director of the Utah Democratic Party. Anderson caused a stir when he starred in a commercial endorsing Republican Mitt Romney for Massachusetts governor.
The mayor's office is a "pretty significant prize to be won," said Monson, who expects "several significant players to get into the race."
People are already lining up. The list of those thinking about running include Salt Lake County Councilman Joe Hatch, state Rep. Ralph Becker and City Council members Dave Buhler, Eric Jergensen and Nancy Saxton. Republican Molonai Hola, who lost in the 2003 mayoral primary, may try again.
Pignanelli is considering another run. And he believes Anderson's possible endorsement of a Republican is a "clever move. This way he can show he's ecumenical. It's all part of a game to keep him a viable candidate for a third term."
Anderson insists he is truly undecided about re-election. "I'm completely up in the air right now," he said. He vows he won't run for a different elected office. And he knows what he wants to do next: create a political advocacy organization to pressure elected officials to work on human rights and environmental causes.
Those are fields he already is pursuing as mayor, to the chagrin of some constituents, and for which he's gaining international attention. Anderson recently was hailed as one of eight "progressive city leaders" by the liberal weekly magazine The Nation because of his commitment to reducing greenhouse gases.
Two members of the European Parliament from Spain and Germany met with Anderson on Wednesday.
Impressed that a mayor off the U.S. coast and from a conservative state committed to the international Kyoto Protocol when he didn't have to, they want Anderson to speak at an upcoming conference in Washington, D.C.
Wednesday's conversation quickly moved outside the boundaries of Salt Lake City, from sprawl in Germany, to genocide in Sudan, to the U.S. embargo on Cuba.
"I love being mayor. I don't enjoy electoral politics," Anderson said later. "That's what I'm debating right now: How much I can get done as mayor versus doing something else."
Tribune reporter Matt Canham contributed to this story.
Lives: In District 7 on the east bench near the Salt Lake City Country Club.
Business: President and founder of Christensen Industries, which manufactures aviation and lighting equipment. Part-owner of Top Stop Convenience Stores.
Family: Married to Kristina Christensen. Three children.
Political experience: Elected to Salt Lake City Council in 1993 and to a second term in 1997. Current member of the SLC airport board.