Berkshire Hathaway's Buffett, Amazon's Bezos and J.P. Morgan's Dimon announced last month a venture designed to cut health costs and improve services for their U.S. employees. The three hope their companies sheer sizes will help bring the necessary scale and resources to tackle the health-care system's most pertinent issues.
"It isn't difficult to shave a little bit off here," Buffett said. "The question is whether we can come up with something better. I'm hopeful, but don't expect any miracles."
Lowering the cost of health care and improving outcomes will be much tougher than it appears, experts say, with health spending representing 18 percent of gross domestic product and is seen as rising.
In an interview on "Squawk Box, " the billionaire investor said health-care spending is a "tapeworm on the economic system." He said the private sector can do more to lower health-care costs than the government can.
He also said the joint venture should have a "top-notch CEO within the year," adding "it has to be someone who really has a grasp on [health care] from every angle."
"We've got the perfect partnership with Jeff and Jamie," he added. "Our companies are big, and yet we can still make things happen. We don't have bureaucratic problems or constituency problems that some others might and we like we each other. We trust each other."
Buffett believes the problem with the U.S. health-care system is it isn't "cost-conscious." The system should deliver "better care in reality and also in terms of how the people feel about the care that they're receiving," Buffett said.
Some analysts speculated that Berkshire's new $377 million stake in drugmaker Teva Pharmaceutical could be related to his health-care cost venture.
Buffett said that would be the "last thing on my mind," saying it was one of his investment deputies who bought Teva. He said the investment deputies didn't tell him and won't if they sell it.
Berkshire disclosed an 18.9 million share stake in Teva as of the end of the fourth quarter, according to the latest securities filing this month. Teva shares popped on the news of the Berkshire investment, but over the 12 months, the stock was still off more than 40 percent.
Buffett was interviewed by CNBC in Omaha, Nebraska, following Saturday's release of his highly anticipated annual letter to Berkshire shareholders.
During the interview, he also spoke on these topics:
— When choosing between stocks and bonds 'I would choose equities in a minute'
— I don't think Berkshire should avoid doing business with people who own guns
— The new GOP tax law benefits Berkshire and acts as a 'huge tailwind' for businesses
— 'We've bought more Apple than anything else' in the last year— Munger's three ways to go broke: 'liquor, ladies and leverage'