President Donald Trump demanded in December that special counsel Robert Mueller be fired and the former FBI director's investigation shut down, The New York Times reported on Tuesday.

At that time, the president was angry over reports that Mueller's latest subpoenas were related to Trump's business interactions with Deutsche Bank, the newspaper said, citing interviews with White House officials.

The Deutsche Bank reports were inaccurate, the special counsel's office told Trump's team, and the president did not act on his desires — but it was the second time that Trump is known to have considered firing Mueller, according to the Times.

The White House did not immediately answer CNBC's request for comment and the special counsel's office declined to comment.

Mueller's office has been focused on investigating Russian interference in the 2016 presidential election and possible collusion with Moscow by Trump campaign officials. The team, which has subpoenaed the Trump Organization, is also believed to be examining whether there was obstruction of justice related to the probe.

Trump has spoken about potentially firing the special counsel as recently as this week.

"Why don't I just fire Mueller? Well, I think it's a disgrace what's going on. We'll see what happens," Trump said Monday in response to a question. "Many people have said, 'You should fire him.'"

If the president were to fire Mueller, financial markets would likely take a tumble.

Read The New York Times' full story on the December episode.

—CNBC's Dan Mangan contributed to this report.