Unlike rival Epic, Oracle Health lost U.S. market share in 2023, according to estimates from KLAS Research. But Ellison's connection to Musk, who is set to co-lead Trump's Department of Government Efficiency, might benefit Oracle Health "if there is a bigger push towards modernizing existing healthcare systems," analysts at Evercore said in a note last week. They recommend buying the stock.

For now, Oracle is busy using AI to rewrite Cerner's entire code base, Ellison said at the analyst event.

"This is another pillar for growth," he said. "I think you haven't quite seen it yet."