President Donald Trump, left, and Jerome Powell, the new chairman of the Federal Reserve on Thursday, Nov. 2, 2017.

U.S. President Donald Trump may be unhappy with Federal Reserve Chairman Jerome Powell, but he has no authority to remove the central bank head from office, Morgan Stanley said.

Still, a new report from Bloomberg cites four sources saying Trump has discussed firing the central bank head.

In fact, Trump has repeatedly criticized Powell, blaming the Fed chair for stock market distress and automaker General Motors' plans to close plants and cut jobs. Powell became Fed chair in February this year after being nominated by Trump and confirmed by the Senate.

"The President can nominate a chair but once the chair is confirmed, the president is out of it and the only way you can remove a chair from office is literally if they broke the law. Congress will have to find a cause to remove them from office through a vote and a procedure," Ellen Zentner, Morgan Stanley's chief U.S. economist, told CNBC's Sri Jegarajah last month.

U.S. law says Fed officials — and those of other independent agencies — can be "removed for cause," according to a report by The Washington Post. The "cause" often means more than a policy disagreement with the president, the Post added.

So far, no Fed chairman has been removed by a president, according to the Post.