One source said aides to the three-term mayor are looking at ballot access issues, but the source refused to speak specifically about what Bloomberg, 73, asked to be done.
The source added that Bloomberg sees the Republican and Democratic presidential races as becoming increasingly polarized, and neither fits Bloomberg's views. But Bloomberg, who has flirted with Oval Office aspirations in the past, is serious about a possible candidacy, the source insisted.
A decision will have to be made by the first week of March, likely before it's clear who the Democratic and Republican nominees are, because of the process to get on ballots for the November election.
A spokesman for the former mayor declined to comment.
News of Bloomberg's consideration was first reported Saturday
morning by The New York Times, which said the media mogul would be willing to spend $1 billion of his own money on a White House bid.
A source close to the former mayor has previously told CNN that Bloomberg would seriously consider entering the race if it appeared Donald Trump or Texas Sen. Ted Cruz would face Vermont Sen. Bernie Sanders in the general election.
Last month, the media mogul commissioned a poll to see how he would fare as a third-party candidate against Trump and Hillary Clinton, the respective Republican and Democratic presidential front-runners, the source close to the former mayor told CNN. The poll was requested after Bloomberg saw Trump's meteoric rise to the top of the GOP field, and he's also eyed a run as Sanders has mounted a serious challenge to Clinton.
This source, however, did not discuss the poll's findings.
Two sources close to Bloomberg said internal polling found that he would theoretically take away more Republican votes from Trump or Cruz than Democratic votes from Sanders. But one source noted, however, that that could change.
Ohio governor and Republican presidential hopeful John Kasich told CNN in New Hampshire Saturday that he isn't worrying about Bloomberg's plans, but added that he likes the mayor.
"I just worry about doing my thing and we'll see what happens. But, you know, he was a good mayor of New York, and if he wants to run, it will probably stimulate the debate. I'm all in favor of that," Kasich said.
Kentucky Sen. Rand Paul, who was also in New Hampshire for a state GOP town hall event, told reporters that a Bloomberg run would split the Democratic vote due to the former mayor's longtime support for greater gun restrictions.
"It seems to be what activated him and inspired him in recent elections has been gun control. So if he splits the Democrat vote, those for gun control, that might be good for Republicans," Paul said.
No stranger to White House speculation
White House whispers surrounding Bloomberg, a longtime Democrat who switched to the Republican Party to seek the NYC mayoralty in 2001, but who ran for his third term as an independent, are not new, and he remains a nationally recognized political figure.
He launched a research effort
into his chances as an independent ahead of the 2008 campaign before ruling out a bid early in the primary fight. He waited until November to endorse President Barack Obama for re-election in 2012, citing climate change in the wake of Superstorm Sandy
And last year, the New York Post reported that New York Democrats approached Bloomberg to gauge his interest in a presidential run
Lately, he has earned conservatives' ire
with his push for greater gun control, and the National Rifle Association launched an ad campaign over the summer accusing him of using his personal fortune to try and strip people of their individual rights and freedoms.