President Donald Trump looks on during the daily briefing on the novel coronavirus, which causes COVID-19, in the Brady Briefing Room of the White House on April 24, 2020, in Washington, DC.

"It is because of President Trump's leadership and relationships that he has brought together government and private industry for an unprecedented collaboration to slow the spread of this unforeseen virus, expand testing capacities, and expedite vaccine development," White House spokesman Judd Deere said. He did not comment directly on the president's calls with these business leaders.

The conversations have ranged from the idea of shutting down the stock market, which did not happen, to discussing the state of the U.S. economy during the pandemic.

There are at least four executives Trump and his team have been in regular contact with, according to the people, who declined to be named due to the private nature of the conversations. They include Blackstone CEO Steve Schwarzman, Oracle Executive Chairman Larry Ellison, Bank of America CEO Brian Moynihan and John Catsimatidis, CEO of New York grocery chain Gristedes. Three of the men – Ellison, Schwarzman and Catsimatidis – are big Trump donors.

President Donald Trump has sought and received advice on tackling the coronavirus crisis in private conversations with several of his allies in the business world, according to people familiar with the matter.

Several executives in touch with Trump are on the president's extensive advisory committee that is focused on working with the White House on how best to revive the economy after the coronavirus forced millions of people out of work.

Take Catsimatidis, who is also a major donor to Trump's reelection effort. As the market fell throughout the month of March, Catsimatidis had an idea that was then brought up to the president: why not order the temporary shutdown of the entire New York Stock Exchange and ground all aircraft for a period of 10 days, according to one of the people. Catsmatidis is not on Trump's advisory counsel.

The airline industry has taken a major financial hit from the pandemic, due to travel restrictions and consumers' fear of traveling while the virus spreads, although all aircraft travel was not shut down. Nor did the markets close.

Catsimatidis was later told by a Trump ally that Wall Street executives had already discussed the idea of closing the markets with White House officials, as stocks plummeted earlier this year, according to a person with knowledge of the matter. The person who described this response would not explain which banks or executives the White House referred to in its response.

Catsimatidis would not discuss his conversations with the president, but did note Trump takes advice from a wide range of people.

"Trump listens to many and always does what he thinks is right," he told CNBC.

Then there's Ellison. The New York Times reported Ellison discussed with Trump the idea of potentially using hydroxychloroquine, an anti-malaria drug, as a coronavirus treatment.

Trump pushed the drug in numerous press briefings, but then stopped after a while. Citing a high risk of death, researchers cut short in April a study of the efficacy of the drug chloroquine, from which hydroxychloroquine is derived.

Those conversations in late March also included the concept of Oracle working with the administration through a donation of a "Therapeutic Learning System." After Ellison spoke with Trump personally about his company's crowd-sourcing platform and how it could help the battle against the pandemic, Health and Human Services said it would use the system.

"The Therapeutic Learning System is a safe, secure web portal designed to gather crowd-sourced, real-time information from doctors and other clinicians about how patients are responding to possible therapeutics to treat COVID-19," the release from April 20 says. "The data will not be owned by Oracle or any other private entity," it adds.

The person familiar with the Ellison conversation, and the later donation to HHS, defended the program.

"It is very important that HHS has analytics of what therapies are actually being practiced by physicians -- patients age, pre-existing conditions, symptoms, severity, ventilator usage, oxygen percentage and therapies," this person said.

Ellison has been a staunch financial supporter of Trump's reelection, including hosting a Trump Victory fundraiser in February. The event, at Ellison's home charged six-figure admission costs and was just a month before states started shutting down due to the pandemic.

A spokesman for Ellison declined to comment.

Schwarzman, CEO of Blackstone, and Moynihan, CEO of Bank of America, have been in touch with Trump and his team on two separate issues.

Moynihan told Trump during an on-camera briefing earlier this month that he and his banking colleagues have spoken with the president's elder daughter, Ivanka Trump, about the best ways to help small businesses through their company's new program, Community Development Financial Institutions.