"He's very frustrated with the Democratic field," Brennan said. "By saying 'maybe,' by going this close ... he can make sure that he's shaping the agenda of who is out there and talking."
Bloomberg has floated the idea of running for president before, but he's never gone this far. He was planning to file paperwork Friday to get his name on the ballot in Alabama, which has the earliest filing deadline for the presidential campaign.
In, Bloomberg's longtime adviser Howard Wolfson said the billionaire and former New York City mayor "is increasingly concerned that the current field of candidates is not well positioned" to defeat President Trump.
"I know close advisers to him have been frustrated particularly with the lack of digital strategy, not matching up to, say, where the Trump campaign is," Brennan said.
"The (Democratic) party in this primary process has been pulled toward … the more progressive wing, to the Elizabeth Warrens, to the Bernie Sanders people, who they identify as populists more than Democrats," she said. "And there's a fear of that among Democratic donors who are more establishment — that they won't be able to be enthusiastic about that candidate."
Though Bloomberg has expressed concern in the past that he could split the vote with former Vice President Joe Biden, who is also seen as more moderate, Bloomberg could give "another voice" to moderate Democrats, Brennan said.
In tweets Thursday, Warren and Sanders responded to Bloomberg's interest in the race.
"The billionaire class is scared and they should be scared," Sanders wrote.
"Welcome to the race, @MikeBloomberg! If you're looking for policy plans that will make a huge difference for working people and which are very popular, start here," Warren wrote, linking to a tax "calculator for the billionaires" on her website.