The Department of Justice will investigate Federal Reserve Governor Lisa Cook based on a criminal referral sent by a Trump administration housing official and arch critic of central bank Chair Jerome Powell , according to a letter obtained by CNBC's Sara Eisen on Thursday.

The letter, addressed to Powell and signed by Justice Department attorney Ed Martin, urges the Fed chair to fire Cook from the board in light of the allegations that have been lodged against her.

"Do it today before it is too late!" Martin wrote.

But Powell does not have the authority to fire Cook: The Federal Reserve Act of 1913 states explicitly that board members can only be removed by the president.

Moreover, the Supreme Court suggested earlier this year that the president does not have the authori

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