President Trump has set up a committee to investigate the mortgage-fraud allegations against Federal Reserve governor Lisa Cook that will hold a White House hearing to consider firing her, according to a notice posted on the White House's website.

Trump called an in-person hearing for Nov. 5, where Cook will be examined by the committee and given a chance to present a defense, the notice said.

The committee will include the assistant to the president for economic policy, the chairman of the Equal Employment Opportunity Commission, and the director of the Office of Government Ethics, the memo said.

"Governor Cook shall appear at the hearing and be examined by the Committee, its representatives, and her legal counsel, if any," said a presidential memorandum dated Oct. 7. "The Committee shall submit written findings of fact and conclusions of law to me and shall recommend whether there is cause to remove Governor Cook from her position."

In a statement, two lawyers for Cook, Abbe Lowell and Norm Eisen, said that they have contacted the White House to "evaluate whether the process proposed has a possibility of being a genuine one and not simply a box checking exercise."

"In light of the President's repeated statements that he has already decided to fire Governor Cook -- regardless of the facts and evidence -- we have grave doubts that this 'hearing' is a legitimate one that would conform to the law," the lawyers said. "But if it is anything close to objective, the conclusion will be that Governor Cook did not commit mortgage fraud, leaving no cause to remove her."

Mortgage-fraud allegations against Cook stem from Trump's long-running attempt to wield more control over how the Federal Reserve sets monetary policy.

Last year, Trump adviser Bill Pulte, the head of the Federal Housing Finance Agency, produced documents that he said showed Cook had listed two separate properties as her "primary residence" on mortgage paperwork. Trump seized on the discrepancy and attempted to fire Cook over the alleged misconduct, a decision he announced abruptly on social media.

Cook was appointed by President Joe Biden to the Fed's board and is serving a term that runs until 2038. She sued to block her firing and has said she never committed mortgage fraud. The laws establishing the Fed say that top officials can be fired only "for cause," a legal term whose application to Fed officials had never been directly tested.

Earlier this year, the Supreme Court ruled for Cook, finding that Trump hadn't provided Cook with a sufficient opportunity to present her case. Trump revived his attempt to fire Cook this summer, sending her a letter outlining the mortgage-fraud allegations that appeared to be an attempt to follow the process requirements that the Supreme Court outlined.