Citing "four people told of the matter," the Times said Trump backed off after White House counsel Donald McGahn threatened to resign. The Washington Post matched that story, citing two sources.
Mueller himself learned about the president's withdrawn directive in recent months, according to the Times.
"We decline to comment out of respect for the Office of the Special Counsel and its process," Ty Cobb, an attorney for the president, said in a statement to the Times.
When asked about the report
At the World Economic Forum at Davos on Friday, Trump scoffed at the report. "Fake news, folks, fake news," he told reporters when asked about it.
Mueller is investigating Russian efforts to influence the 2016 election and whether the Trump campaign colluded with the Kremlin. The probe has dogged and frustrated Trump, and has also moved into whether the president has obstructed the investigation.
Others suggested last year that the president was thinking about firing Mueller, with one ally telling PBS in June that Trump was "considering perhaps terminating the special counsel. I think he's weighing that option."
In August, however, the president claimed he had never even considered firing the special counsel. "I haven't given it any thought. I mean, I've been reading about it from you people. You say, 'Oh, I'm going to dismiss him.' No, I'm not dismissing anybody. I mean, I want them to get on with the task, but I also want the Senate and the House to come out with their findings."