The chances that another major contender decides to run are remote: While Mrs. Clinton and Mr. Bloomberg have both been encouraged to enter the race, Democrats close to them believe the only scenario under which they’d consider running is if Mr. Biden drops out or is badly weakened.

Neither is likely to take place before the end of this calendar year, at which point the filing deadline to be on the primary ballot in large Super Tuesday states like California and Texas will have passed. But that’s not stopping the speculation, which has only grown of late thanks in part to the 2016 Democratic nominee’s public comments.

Mrs. Clinton, after largely staying in the background of the Democratic primary , has been more vocal this month, promoting a book she wrote with her daughter and taunting Mr. Trump on Twitter. She also opened a feud with Representative Tulsi Gabbard of Hawaii by claiming the long-shot candidate was being supported by the Russians, as a potential third-party spoiler in the general election.

Democrats who have recently spoken with Mrs. Clinton say she shares the same concerns other party elites have about the field — worried about Mr. Biden’s durability, Ms. Warren’s liberal politics and unsure of who else can emerge to take on Mr. Trump. But these people, who spoke anonymously to discuss private conversations, say she enjoys the freedom that comes with not being on the ballot.



Mr. Bloomberg is said to be more eager to find a way into the race — and chatter about his potential candidacy has only grown among Democrats who work on Wall Street and are concerned about Ms. Warren’s rise. He raised some eyebrows recently by putting off a fund-raising request from one third-party Democratic group until he knew about his own intentions, according to two Democrats familiar with the conversation.

But the former New York mayor has flirted with presidential runs before, only to pull back. Friends say he recognizes his long odds at this stage of the race and his advisers suggest he will play a significant financial role in the 2020 race without his name on the ballot.