In a news conference in New York City, the President-elect stressed that legislation to repeal President Barack Obama's signature health care law -- along with legislation to replace it -- will be considered "essentially simultaneously."
"We're going to be submitting -- as soon as our secretary's approved, almost simultaneously, shortly thereafter, a plan. It'll be repeal and replace. It will be essentially simultaneously," Trump said. "Probably the same day, could be the same hour."
Price, a Georgia congressman, has been one of the most ardent Obamacare critics and is among the few to introduce more detailed legislation to repeal and replace the law. His confirmation hearings will begin next week.
At the news conference, Trump also expounded on the political liability that comes with trying to overhaul the Affordable Care Act, saying that for the time being, the healthcare law is Democrats' problem to "own."
"We don't want to own it. We don't want to own it politically. They own it right now," Trump said. "The easiest thing would be to let it implode in '17."
Price introduced legislation in 2015 that bears many similarities to Trump's vision for health care reform and to House Speaker Paul Ryan's overhaul proposal.
Like many Republican proposals, Price would give refundable tax credits to those who buy policies in the individual market based on their age. He would reverse Medicaid expansion and provide many incentives and protections for Health Savings Accounts, a favorite Republican policy.
Trump and Republicans have also promised to provide some protection for Americans with pre-existing conditions. Price's proposal is not as comprehensive as Obamacare's, which bans insurers from discriminating against the sick.
Instead, Price would require carriers to insure Americans with pre-existing conditions as long as they have maintained continuous coverage. Those who don't meet that criteria could be charged higher premiums or be forced to look to state high risk pools, which were largely eliminated under Obamacare, to provide coverage.
Trump told the New York Times this week that he wants Republicans to vote immediately to both repeal and replace Obamacare -- even as quickly as next week.
But Republicans on Capital Hill are not close to having a replacement plan ready, and don't expect to vote on a budget reconciliation bill that would repeal major portions of Obamacare until late February or March. At that point, Republicans plan to begin considering a series of possible legislative paths to replace what they voted to repeal.
It's also not clear that there will ultimately be one comprehensive "replacement" bill -- in fact, GOP leaders are currently weighing various legislative paths to incrementally replace what they roll back.
For example, they are exploring what replacement measures could potentially be inserted into the "repeal" reconciliation bill. Leaders are also looking at whether any replacement or healthcare reform measures could be inserted into reauthorization bills that Congress is expected to take up later this year.