Bloomberg made the decision over the weekend and will announce it Thursday, according to the person, who has been briefed on the matter but spoke on condition of anonymity because the announcement hasn't been made. The person said the mayor has been wrestling with the decision for the past couple of months.
The billionaire former CEO will cite the nation's precarious economic situation as the reason that New York needs a tested financial manager to stay and guide the city, the person said.
The mayor, founder of the multibillion-dollar financial data firm Bloomberg LP, is reported to be worth an estimated $20 billion.
News of Bloomberg's decision was first reported by The New York Times.
The move is risky because the mayor would be going against both his own prior support of term limits and polls that show the public supports the voter-approved law.
The individual close to the mayor said Bloomberg's plan is go through the City Council to amend the law to allow a third term because it is too late to get the issue on this year's ballot. A Times survey of council members last month found that a majority were willing to amend the term limits law.
Chris Kelley, associate director of the government watchdog group Common Cause New York, accused Bloomberg of attempting to subvert the will of the voters.
"If there's a discussion that needs to be had about term limits, the mayor has had years in office during which we could have had a public discussion," Kelley said. "We are now faced with a situation where we are looking at economic crisis and massive turnover at City Hall ... and to make an end run around the voters' choice is just incredibly disappointing."
When Bloomberg vetoed a bill in 2002 that would have extended the terms for some officials, he said the proposed law amounted to changing the rules for personal political gain. In recent months, however, the Democrat-turned-Republican-turned-independent hinted that he'd be willing to overturn the measure.
Bloomberg's change of heart comes amid the nation's worst financial emergency since the Great Depression. The turmoil has dealt a serious blow to the city's economy, which relies on heavily on Wall Street profits for its tax base.
The crisis had led at least one major supporter of term limits to support a third term for Bloomberg.
The New York Post reported Tuesday that billionaire cosmetics heir Ronald Lauder, who spent millions on the referendum that led to the enactment of the two-term limit in 1993, was willing to make a one-time exception for Bloomberg.
"I've been reading that Mayor Bloomberg might be interested in serving a third term," Lauder told the Post. "Because of the unprecedented times, this is welcome news. To me, Mayor Bloomberg's brilliance in the financial sector, particularly Wall Street, would be invaluable."
Just weeks ago, Lauder's spokesman announced that he would bankroll television commercials arguing that term limits were still needed. Lauder's office and his spokesman didn't immediately return calls from the AP on Tuesday.
Mark Green, the former city public advocate who lost to Bloomberg in 2001, called the mayor's move "an antidemocratic, unfeeling, power grab."
Green, now president at Air America Media, said civic and labor officials had discussed mounting a pro-term-limits campaign should Bloomberg seek to overturn the law.
"He's picked a fight. And now he'll get one," he said.
Dick Dadey, executive director of the good-government group Citizens Union, said that any change to the law should be made by voters, not legislators. "There are compelling reasons to consider changing the law. But the will of the voters is sacrosanct on this issue," he said.
Not even 9/11 swayed the support many New Yorkers have for the term-limits law.
With his second term nearly over, then-Mayor Rudolph Giuliani suggested overturning the term-limits law but ultimately decided against it. Even in the wake of the attacks, with Giuliani's approval rating at 90 percent, one poll found that 55 percent of New York City voters opposed repealing term limits.
Any change in the law would send shock waves through the ranks of the city's politicians, many of whom have been campaigning for different jobs, including Bloomberg's. The law currently on the books will force the mayor from office at the end of next year, as well as the city comptroller, two-thirds of the city council and the city's public advocate.
Democrats lining up to run for mayor include city Comptroller William Thompson, city council speaker Christine Quinn, U.S. Rep. Anthony Weiner and city councilman Anthony Avella. On the GOP side are supermarket magnate John Catsimatidis and lawyer Bruce Blakeman.
Bloomberg spent some $155 million on his first two campaigns, winning re-election by 20 percentage points in 2005.
John Collins, a spokesman for Weiner, said the news did not change the Queens congressman's intention to run for mayor.
"This is highly speculative," Collins added. "It's illegal to run for a third term."
Thompson called Bloomberg's plan a "terrible idea."
"This isn't about a person," he said. "Other leaders could move this city forward also."