The Trump administration has been working behind the scenes for months on a strategy to force greater price disclosure across much of the $3.5 trillion health-care industry. The push relies on existing administrative tools, according to people familiar with the discussions. Those include Labor Department powers under the law setting minimum standards for private-industry health plans and current hospital-payment rules under Medicare. The administration is strongly interested in forcing insurers to publicize the negotiated rates they pay for services, the people said. The requirement could affect insurers providing coverage in the private-employer market.