Mr. Bloomberg, the former New York City mayor and billionaire businessman, has been privately weighing a bid for the White House for weeks and has not yet made a final decision on whether to run, an adviser said. But in the first sign that he is seriously moving toward a campaign, Mr. Bloomberg has dispatched staffers to Alabama to gather signatures to qualify for the primary there. Though Alabama does not hold an early primary, it has a Friday deadline for candidates to formally enter the race.

Should Mr. Bloomberg proceed with a campaign, it could represent a seismic disruption in the Democratic race. With his immense personal wealth, centrist views and close ties to the political establishment, he would present a grave and instantaneous threat to former Vice President Joseph R. Biden Jr., who has been struggling to raise money and assemble a ideologically moderate coalition.