Price has taken 26 flights on private jets since May, according to a Politico investigation. In two instances, Price mixed official business with personal travel, the website reported Tuesday.
In June, he traveled on a $17,760 round trip flight from Washington to Nashville and spent only 5½ hours there, Politico reported. He had two official visits and then had lunch with his son during the trip, it said.
In one four-day stretch, his flights cost an estimated $60,000, according to Politico. Some of those flights came at times when dramatically cheaper commercial air travel would have been available.
Asked about the report as he left for a speech in Indiana on his tax reform plan, Trump said: "I am not happy about it, and I let him know it."
Asked if he would fire Price, Trump responded, "We'll see."
Price and Trump have repeatedly urged fiscal discipline from the government.
The Department of Health and Human Services has said Price's travel does not violate federal travel regulations. The HHS inspector general is examining the flights.
Price has "heard the criticism and the concerns," and took the matter "very seriously," Caitlin Oakley, press secretary for HHS, said in a statement.
Oakley said HHS supported the current review of the travel.
"The Secretary has initiated an internal departmental review of the procedures and processes that we go through for official travel to determine whether there are any changes or reforms that are necessary," she said.
Price, a former congressman from Georgia, is a leading proponent of repealing and replacing the Affordable Care Act. Three Republican attempts to repeal it have failed, including one this week.
Before joining the Trump administration, Price came under fire for buying shares in a biotechnology company at a discounted rate while sitting on a committee that could influence its stock price.
Price eventually sold his stake in the company during the HHS confirmation process and made a profit of at least $150,000, according to The Washington Post.
Through a spokeswoman, Price denied that he had invested in non-public information.