President Donald Trump is considering taking the unprecedented step of firing Federal Reserve Chairman Jerome Powell over the central bank's moves to hike U.S. interest rates, sources told Bloomberg News.

Bloomberg cited four unnamed persons with knowledge of the situation as saying the president has talked in recent days about sacking the Fed chief, whom Trump appointed. While it's unclear if the president has legal authority to fire the Fed chair, none ever has.

CNBC, meanwhile, reported that when asked Saturday, White House Press Secretary Sarah Huckabee-Sanders said she was not aware of any plans to fire Powell.

The Bloomberg report comes after months of head-butting between the president and the central-bank chief. At one time of growing frustration in October, Trump reportedly called Powell "crazy."

Bloomberg said the White House and Fed declined to comment on the matter, but sources told the news agency that the president recently mentioned several times the possibility of letting Powell go. However, the sources also said that Trump's aides consider it unlikely that the president will ultimately do so.

Such a move could roil markets at a time when volatility and uncertainty already rule Wall Street. Investors are facing a swooning stock market, a U.S.-Chinese trade war, top White House officials' exits and a federal-government shutdown.

"While I can understand the president's frustration given that he likes to use the stock market as a barometer of his presidency, if he were to focus on the data of late he would likely realize that Fed Chairman Powell is signaling a softening toward rising interest rates in 2019," said Chris Versace, chief investment officer at Tematica Research and a columnist for TheStreet's Real Money premium site for active traders. 

"Trump also has to consider what it would mean to the market in terms of uncertainty were he to formally consider removing Powell," Versace said. "The market is grappling with a number of issues and uncertainties as it is, and removing a Fed chair that has been on the job for just under a year would only add to them."

(This article has been updated.)