Former Vice President Joe Biden (D) speaks about the Coronavirus and the response to it at the Hotel Du Pont in Wilmington, DE.

Joe Biden has said that he's started discussing with his advisors who he would ask to join his administration if he goes on to defeat President Donald Trump in November.

His donors, on the other hand, have been privately floating some names that they hope to see become advisors for the campaign or even join a Biden White House, particularly as the coronavirus rattles the economy, according to people with direct knowledge of the matter. The people declined to be named because discussions were in private.

According to the people, the names being discussed by donors and supporters alike include Sens. Kamala Harris, D-Calif., and Elizabeth Warren, D-Mass.; BlackRock CEO Laurence Fink; Blackstone Executive Vice Chairman Tony James; Mark Gallogly, the co-founder of investment firm Centerbridge Partners; and Roger Altman, the founder of Evercore, among others.

Gallogly and Altman have helped Biden raise campaign cash throughout the 2020 election cycle, while James backed former South Bend, Indiana, Mayor Pete Buttigieg when he was in the race for president.

If Biden doesn't choose Harris as his running mate, some privately said that she should be attorney general. Warren could be a key campaign economic advisor, others said. Fink would be a great pick for Treasury secretary, while Gallogly and James could be strong players in that department as well, these people noted.

Robert Wolf, a longtime Democratic donor and confidant of President Barack Obama, told CNBC that although he's not aware of the discussions taking place about Fink, he believes he would be a great pick for the job.

"There would be many great choices, but certainly Larry would be one of the top choices for anyone's list," he said.

The deliberations about who could join forces with Biden come as the coronavirus pandemic spreads across the country and lays siege to the economy. Democrats are hoping that, if Biden can defeat Trump, his administration will have the people in place that could help get the economy back on track. Almost 10 million Americans filed for unemployment benefits in just two weeks in late March, and markets have been in flux.

The former vice president is ahead in the delegate count but is still in a primary fight against Sen. Bernie Sanders.

Though donors are not official members of the campaign, they often have a direct line to candidates themselves and could be key influences when Biden moves ahead with choosing who to bring on as advisors.

The Biden campaign and all the business leaders mentioned in this story did not respond to requests for comment. Representatives for Harris and Warren did not respond to requests for comment.

Biden told his fundraisers during his virtual event on Friday that, while he has not started to interview or vet members of a possible future administration, he's inquiring among advisors about whether some people would follow him into a government role if he were to become president. Biden's campaign has gone fully virtual in the wake of COVID-19 and has been pushing for Trump to act faster when it comes to his response to the pandemic.

"There are a number of people like you, and I'm not being a wise guy, who have been helping me, they're serious people who I've had discussions with about whether or not — not a cabinet position, because there's nothing quid pro quo — but asking them are they willing to come into a government if I get elected," Biden told his donors last week, according to a transcript of the meeting provided by the pool reporter.

"I haven't asked anybody — no discussion yet — but who would I ask to be secretary of State? Who would I ask to be the attorney general? Who would I ask to be White House counsel? Who would I ask to be the chief of staff?" Biden continued.

Some of Biden's business allies have started pushing for Harris to be his pick for vice president. Yet if she doesn't become his running mate, they are looking to approach the campaign about her being picked for attorney general, noting her experience in the same role for California, the country's most populous state.

Many of the top financiers for Biden and the Democratic Party are starting to warm up to Warren potentially becoming an economic advisor for the campaign. Most of these big-money donors saw her as their arch nemesis when she was running for president. At the time, she was pitching raising taxes on wealthy Americans and historically has been a staunch critic of the U.S. banking system. While she was rising in the primary polls, donors told CNBC that they were warning party leaders that if she became the nominee they would back Trump instead.

Still, these people say that with the bipartisan effort in Congress to protect small businesses, through a $2 trillion stimulus package, Warren's economic policy proposals may now have an even broader appeal to a larger swath of the electorate. Biden has already endorsed Warren's bankruptcy plan that would allow those with student debt to get some relief through bankruptcy.

Warren, in a recent interview with Vox, touted her belief that the federal government must lead the way in giving financial aid to those suffering economic hardships from the coronavirus.

"Only the federal government can cushion the economic blow here in a meaningful way," Warren said. "It is only the federal government that can actually print money in a time of crisis. Only the federal government that can deficit spend," she added.

Though she has not officially endorsed Biden, she came very close to backing his campaign in an interview on SiriusXM when she was asked about having any interest in a future Democratic cabinet position.

"I think we've got someone like Joe Biden in there, we're going to have good, strong people. For me, and I appreciate the kind and generous words, but right now, and we are in the middle of this crisis and that's where I'm keeping my focus," she said.

Fink, who reportedly told Biden "I'm here to help" before he officially announced his run for president in April 2019, is being touted among financiers and among the vice president's allies as someone who could be a solid pick to lead the Treasury Department. Fink supported Hillary Clinton during the 2016 presidential election and many were pushing him to be her choice for that position before she fell to Trump.

In 2012, as Tim Geithner was wrapping up his term as the head of Treasury under Obama and heading to the private sector, Fink kept the door open to taking the position. Fink said at the time that he would "certainly take the call, and I would be a good listener" but noted he was happy at BlackRock.