Administration officials are discussing replacing Health and Human Services Secretary Alex Azar following criticism of his management of the early response to the coronavirus pandemic, according to six people familiar with the discussions.

It remains unclear if Mr. Azar will be ousted and in what timeline that might occur. Administration officials said the White House is hesitant to shake up the leadership of HHS during a pandemic, though they acknowledged that frustration with the secretary has been growing in recent weeks.

President Trump is prone to unexpected staffing moves and dismissals, so the decision could still go either way. But people familiar with the discussions say they have accelerated in recent days with a far more serious tone, amid mounting criticism about Mr. Azar’s leadership, including a report in The Wall Street Journal detailing his early missteps in the coronavirus response.

The president has publicly indicated his own frustrations with Mr. Azar, tweeting earlier this month in response to reports that Mr. Trump didn’t act early enough to respond to coronavirus that Mr. Azar “told me nothing until later.”

In a tweet on Sunday, Mr. Trump said reports that Mr. Azar would be fired were “fake news.” He said the secretary was doing an “excellent job.”