"He certainly believes he has the power to do so," White House press secretary Sarah Sanders said when asked if the president believes he has that power.
The administration had been denying for months that Trump is considering firing Mueller. The change in tone followed Trump's anger over an FBI raid of the office of Michael Cohen, his long-time personal lawyer.
After receiving a referral from Mueller, federal prosecutors in Manhattan on Monday obtained a search warrant, raided Cohen's office and seized emails, tax documents, business records and communications between Cohen and Trump.
But the raid reportedly does not appear to be directly related to Mueller's investigation, which focuses on alleged Russian meddling in the 2016 US presidential election and possible collusion between the Trump campaign and Moscow.
"It's an attack on our country in a true sense. It's an attack on what we all stand for," Trump said after knowing the operation. "We'll see what happens," he said when asked if he would fire the special counsel, who reports to Deputy Attorney General Rod Rosenstein.
"I think that the president has been clear that he thinks that this has gone too far," Sanders said of Trump's remarks.
CNN reported Tuesday that Trump, who does not have the power to fire Mueller directly, is considering firing Rosenstein, who could remove the special counsel for misconduct or other reasons, in a bid to put greater limits on the ongoing Russia probe.
Mueller has so far charged 19 people, among whom were several Trump campaign associates that have pleaded guilty to various charges stemming from Mueller's investigation. They are all cooperating with prosecutors but none of the charges are directly related to the collusion allegation.
It was reported earlier this month that Mueller told Trump's lawyers that the president is not a criminal target of the Russia probe, but stressed that he remains a subject of the investigation.