“We’re making a lot of progress, and I think we’ll probably have a CEO within a couple of months,” Buffett said at the Berkshire Hathaway meeting in Omaha.

The legendary investor, nicknamed the “Oracle of Omaha,” did not specify who was in the running for the top position. But candidates under consideration reportedly include Todd Park, the federal government’s former chief technology officer; Andy Slavitt, the former acting administrator of the Centers for Medicare and Medicaid Services; and former Aetna executive Gary Loveman, according to CNBC.

While few details of the healthcare venture have been released so far, Buffett also clarified the nature of Berkshire’s partnership with Amazon (AMZN) and JPMorgan (JPM).

“We don’t plan to start healthcare companies or necessarily insurers or anything,” Buffett said at the Berkshire meeting. “The motivations are not primarily profit-making. We want our employees to get better medical service at a lower cost. We’re certainly not going to come up with something where we think the service that they receive is inferior to what they’re getting now, but we do think that there may be ways to make a real significant changes that could have an effect.”

Buffett acknowledged that the task will be extraordinarily challenging, and “the resistance will be unbelievable.” But he said that the venture’s success will depend heavily on their CEO selection, “and whether that person will have the imagination, and support of people that will enable us to make any kind of significant improvements in the system.”

At the moment, the healthcare triumvirate is focused on delivering cheaper, better care to the more than one million employees of Amazon, Berkshire Hathaway and JPMorgan — though “a flood” of other companies have expressed interest in joining, Buffett said. “There isn’t anything to join into now,” he explained. “But there will be if we come up with any ideas that are useful, and whether we can bring the resources, bring the person—and the CEO is terribly important.”

Despite the difficulty U.S. lawmakers and companies have had in stemming the tide of rising healthcare costs — which Buffett calls “a tape worm” on American business and its competitiveness — the investor believes that the unique combination of Berkshire Hathaway and its partner corporations may finally be able to make progress where others have failed.

“I think there is some chance we will do something, there’s a chance nobody quantified that we can do something significant, and we are positioned better than most people to try,” Buffett said.

One way the partnership is already doing something different from prior efforts by governments and insurers: Buffett, Amazon CEO Jeff Bezos and JPMorgan’s Jamie Dimon are eschewing bureaucracy and paperwork. “We don’t have a partnership agreement among us,” Buffett said. “Somebody started drawing up one in the legal department and the CEO just put at stop to it.”

Added Buffett, “If we fail, I hope somebody else succeeds.”