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Trump is set to name Republican Representative Tom Price, an orthopedic surgeon from Georgia, as his Health and Human Services secretary, and consultant Seema Verma to lead the Centers for Medicare and Medicaid Services (CMS), a powerful agency that oversees government health programs and insurance standards.
He is expected to cast Price and Verma as a "dream team" to help him once he takes office on Jan. 20 with his campaign pledge to repeal President Barack Obama's signature health law, the Affordable Care Act that is better known as Obamacare.
Trump has said he will replace Obamacare with a plan to give states more control over the Medicaid health plan for the poor and allow insurers to sell plans nationally.
Both positions require Senate confirmation and the Trump administration will need to have agreement from the Republican-led U.S. Congress to repeal and replace the health law.
Price, an early Trump supporter from the U.S. House of Representatives, is currently the chairman of the budget committee. He has long championed a plan of tax credits, expanded health savings accounts, and lawsuit reforms to replace Obamacare.
Verma worked with Vice President-Elect Mike Pence, the governor of Indiana, on a compromise to expand Medicaid coverage for the state's poor with federal funding.
The Indiana program requires beneficiaries to make monthly contributions to health savings accounts.
Price campaigned with Trump because he promised to overhaul Obamacare. However, Trump's position on the health insurance program appeared to soften after he met Obama following the hard-fought Nov. 8 election.
Trump said he would consider keeping provisions in the law that let parents keep adult children up to age 26 on insurance policies and bar insurers from denying coverage to people with pre-existing conditions.
Price and Verma are two of about 70 people who Trump has met so far as he looks to shape his White House and Cabinet team.
Trump is expected to reveal an additional Cabinet pick on Tuesday, but is not expected to announce his choices for the three biggest positions - state, defense and treasury - as he continues to consider his options.
After seeing retired general David Petraeus on Monday - a potential candidate for the State Department or the Pentagon - Trump is expected to meet U.S. Senator Bob Corker of Tennessee, the chairman of the Senate Foreign Relations Committee on Tuesday, and later have dinner with Mitt Romney.
Romney, the 2012 Republican presidential nominee, and Corker are in the running for secretary of state, along with former New York Mayor Rudy Giuliani.