"I am not happy with him," Mr. Trump said of Price, who left Congress earlier this year to join the Trump Administration.
Asked by reporters if he might fire Price, the President left his HHS chief hanging.
"We'll see," Mr. Trump said.
The President's comments came hours after the House Oversight Committee signaled that it was reviewing press reports about private charter jet trips taken by Price and other top officials in the Trump Administration.
"The Committee is examining the extent to which non-career officials at federal departments and agencies either use government-owned aircraft for personal travel or private non-commercial aircraft for official travel," read a bipartisan letter sent to the White House Chief of Staff.
Signed by Rep. Trey Gowdy (R-SC) and Rep. Elijah Cummings (D-MD), the letter is the clearest signal yet that Congress is raising red flags about private charter travel, detailed in recent stories about HHS Secretary Tom Price, EPA Administrator Scott Pruitt, and Treasury Secretary Steven Mnuchin.
Gowdy and Cummings - the top two members of the House Oversight Committee - asked for documents and information on such flights by October 10.
Democrats also pounced, with former colleagues in the Congress calling for Price's resignation.
"The American people deserve cabinet secretaries who place the public good above their own private interests," said Rep. Ruben Gallego (D-AZ), who said Price "should resign immediately."
Last week, when stories first emerged about travel by Price on charter flights, officials at the Department of Health and Human Services defended his decision to take private jets instead of commercial flights.
"The travel department continues to check every possible source for travel needs including commercial, but commercial travel is not always feasible," the statement read.
But those answers did not mollify the President, who was reported by some news organizations to be very unhappy with Price - and then showed it.
"I'm not happy about it," the President said when asked about Price, though Mr. Trump has made his anger known about other top officials in his administration - like Attorney General Jeff Sessions - but not forced them out of a job.
On Capitol Hill, members of the Georgia delegation were reluctant to criticize their former colleague.
"I don't really have a comment on that, I think that's something that they're investigating now, and we'll see what happens," said Rep. Doug Collins (R-GA).
"I really don't know the details, so I'll reserve judgment," said Rep. Barry Loudermilk (R-GA).
"I'm sorry to hear of it, but I'm sure they'll get it worked out," added Rep. Buddy Carter (R-GA).
Now they wait to see if Price survives or not.
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