Former New York City mayor Michael R. Bloomberg is considering an independent campaign in this year’s presidential race. (Spencer Platt)

Michael R. Bloomberg, the billionaire and former New York mayor, is considering making an independent bid for the presidency, a move that could provide yet another wild turn in a 2016 race that has already seen more than its share of them.

Bloomberg’s deliberations, first reported by the New York Times, were confirmed Saturday by several close associates.

Bloomberg has explored the possibility before, always making a pragmatic calculation of whether winning is feasible. Three associates said that several factors have convinced him that a run outside of the Republican and Democratic party processes is worth another look.

One factor is the possibility that the Republican nomination could be won by a polarizing figure, such as fellow New York billionaire Donald Trump or Sen. Ted Cruz (Tex.), the two leaders of the GOP race heading into the Feb. 1 Iowa caucuses.

Trump, once expected to be a temporary phenomenon, has dominated the large GOP field for so many months that it is no longer assumed that the Republican establishment will be able to stop him. Cruz, the tea party upstart, may be even less acceptable to the GOP leadership against which he has so often rebelled.

The other factor is that the Democratic front-runner, Hillary Clinton, may turn out to be a weaker candidate than was once expected — and might even lose the nomination to Sen. Bernie Sanders (I-Vt.), a self-described democratic socialist whose mainstream appeal is in question.

If the right combination of those possibilities begins to look likely — which Bloomberg thinks could become apparent in March, after the first big round of state primaries — he believes they could create an opening for him to make a credible run as an independent.

“It’s something that he’s looked at, off and on, for years, and every now and then, he polls. At one point, he concluded it just couldn’t be done,” said one Bloomberg friend, speaking on the condition of anonymity because of the political sensitivities involved.

But with the unexpected upheavals that appear to be taking place in both parties, the friend said: “What you have is some stirrings, and people taking some fresh looks.”

In addition to his considerable financial resources, Bloomberg has a reputation as a skilled manager and political bridge builder. A longtime Democrat, he switched to the Republican Party to run for mayor in 2001. Six years later, he changed his registration to independent.

Bloomberg made his fortune by founding the financial news and information company that bears his name. It has made the desktop Bloomberg terminal all but indispensable for those who make their money off of real-time financial data.

He took office less than four months after New York was traumatized by the Sept. 11, 2001, terrorist attacks, pledging that the city would remain “safe, strong, open for business and ready to lead the world in the 21st century.”

When Bloomberg left the post 12 years later, New York was thriving by most measures: The economy was robust, crime was down, the transportation system was more efficient, and a budget deficit estimated at more than $3 billion when he took over had transformed into a $2.4 billion surplus.

The biggest blot on Bloomberg’s mayoral record was authorizing an aggressive policing tactic, known as “stop and frisk,” which was found unconstitutional by a federal court that said it was used in a discriminatory way against law-abiding citizens, most of them black or Hispanic.

The former Republican has moderate views on social issues. In 2014, he launched a $50 million effort to take on the National Rifle Association on gun control — an issue that Clinton has also emphasized in her campaign.

Word of Bloomberg’s deliberations come with the first contest in Iowa a little more than a week away, and at a tense moment for Clinton. The former secretary of state, once viewed as all but invincible in her second bid for the Democratic nomination, has seen much of the energy in the race shift toward Sanders. He has closed the gap with her in polls out of Iowa and enjoys a comfortable lead in New Hampshire.

Senior Democrats say that something close to a panic is setting in among party fundraisers and interest groups that have invested heavily in Clinton’s candidacy.

“There’s no question in my mind that there is real worry,” a longtime Clinton ally and adviser said. He spoke on the condition that he not be identified, for fear of offending her.

“There are so many parallels to 2008,” the Clinton ally added, referring to the race in which she had begun as the front-runner but lost to first-term Sen. Barack Obama of Illinois.

Should Bloomberg decide to enter the race, he would be up against a formidable set of challenges, starting with the fact that no third-party contender has ever won the White House. The most successful of them — including former president Teddy Roosevelt in 1912 and businessman H. Ross Perot in 1992 — are remembered mostly for having drawn off votes from one of the major parties, throwing the election to the other.

News that Bloomberg was considering a run set off alarm bells among Democrats in particular. Dan Pfeiffer, former Obama White House communications director, tweeted Saturday afternoon: “Bloomberg running for President would almost certainly hand the [White House] to the GOP. If no one gets 270 [electoral votes], GOP congress picks the prez.”

Bloomberg also is not all that well known outside the political circles of the Northeast. An April 2014 poll by NBC News and the Wall Street Journal found that 18 percent of those surveyed had a favorable view of him, 28 percent had a neutral one, 26 percent had a negative opinion. However, 28 percent said they were not familiar with his name or were not sure how they viewed him.

The Times reported that Bloomberg has retained a consultant to help him figure out what it would take to get his name on the ballot in all 50 states, and that he will also do another round of polling after the Feb. 9 New Hampshire primary to assess whether voters might have an appetite for him to enter the race.