Joe Biden's allies are becoming increasingly concerned that a Mike Bloomberg candidacy could take votes away from the former vice president and help Sen. Elizabeth Warren win the race for the Democratic presidential nomination.

Bloomberg's political aides confirmed that he's again considering entering the 2020 race, after he decided against it in March. Top Bloomberg advisor Howard Wolfson said Thursday that the billionaire former New York mayor is "increasingly concerned that the current field of candidates is not well-positioned" to defeat President Donald Trump next year.

Biden told reporters on Friday that he welcomes Bloomberg, a fellow moderate, into the race. Yet several of his supporters see the former mayor's move as potentially giving an edge to Warren, a liberal populist.

"This hurts Biden tremendously," said one of Gov. Andrew Cuomo's outside advisors. Cuomo has encouraged his vast donor network to back the former vice president. "Even if he doesn't get it," this person added, "the whole thing plays that Biden is weak. It cements in people's minds that Biden can't make it work."

Bloomberg is already gaining the support of people on Wall Street, a core source of fundraising for Biden. Billionaire Leon Cooperman endorsed Bloomberg him before he even officially jumps into the primary. Biden's closest supporters largely agree that Bloomberg and Biden would likely split moderate voters in the party.

Democratic voters who identify with middle-of-the-road policies have been a key constituency for Biden's candidacy. Recent New York Times/ Siena College polls show Biden ahead of all the other candidates in favorability in the key battleground states of Arizona, Florida, Michigan, North Carolina, Pennsylvania and Wisconsin. That same surveys show that a majority of participants want a moderate candidate and one that will find common ground with Republicans.

Bernard Schwartz, a Biden supporter and CEO of BLS Investments, said that Bloomberg's possible candidacy could give a boost to Warren, who has made targeting billionaires a key part of her appeal.

"I think it takes away from [Warren's] biggest competitor, and that's Joe Biden. I'm not saying Bloomberg is doing it intentionally, but that what I think the result would be," he said. "I think Bloomberg was a great mayor, but I think he's making a mistake. If you have a few billion dollars you can do what you want to do."

Other Biden supporters are skeptical that Bloomberg will actually be a viable candidate.

"I see his move as a placeholder until we get clarity on Joe's viability," one of Biden's top fundraisers said about Bloomberg's recent move. This person spoke on the condition on anonymity in order to speak freely.

Some Biden supporters painted Bloomberg as an indecisive, wavering politician.

"I think it's ridiculous and I think ultimately, 45 days from now, I don't think Bloomberg will be a candidate," said a Wall Street banking executive backing Biden who declined to be named. "Can I remind everyone he was a Republican before he became a Democrat? Can I remind you that the Democratic Party of 2020 is not rallying around billionaires?" this person added.

As mayor of New York, Bloomberg was first a Republican and then later became an independent. Bloomberg switched to the Democratic Party a month before last year's midterm congressional elections.

"He's like Mario Cuomo or even Hamlet on the Hudson. He's in, he's not in. Until I see real proof he's in then I don't believe it," said a lobbyist helping Biden behind the scenes. Cuomo, the late former New York governor and father of Andrew Cuomo, famously agonized over whether to run for the Democratic nomination in the 1992 race before ultimately deciding not to.

Representatives for Biden and Bloomberg did not return a request for comment.

Political strategists from both sides of aisle see a Bloomberg candidacy ultimately hurting Biden. But they also broadly acknowledge that the former New York mayor doesn't have a chance to win a primary with formidable candidates, including democratic socialist Sen. Bernie Sanders, pushing progressive policies.

"Biden's doing enough to hurt himself right now. It could accelerate his demise," Democratic strategy Mary Anne Marsh told CNBC. "I think Bloomberg's premise is flawed. If he could pick up Joe Biden's supporters, [Pete] Buttigieg supporters, Kamala Harris supporters, Amy Klobuchar supporters, Cory Booker's supporters, those aren't transferable," she added.

"No shot a billionaire who still supports stop-and-frisk wins the Democratic primary. And a third party run would just reelect Trump," said Chapin Fay, who was a media advisor for GOP billionaire and former New York mayoral candidate John Catsimatidis.

The stop-and-frisk policy allowed New York police officers to search or detain anyone them deem suspicious. Bloomberg defended the tactic earlier this year.

Meanwhile, some Biden fundraisers seem to be shrugging off any effect Bloomberg may have on their candidate's campaign.

During a conference call Friday with Biden's top financiers in California, bundlers discussed ways they can start focusing on trying to siphon donors and fundraisers from Sen. Kamala Harris, according to people familiar with the matter. These people said Biden financiers are looking to reach out to Harris' lead fundraisers in her home state before they get behind Warren.

Bloomberg did not come up on the call, they added.