Cook responded to Pulte in a statement, "I have no intention of being bullied to step down from my position because of some questions raised in a tweet."

A new report says the president might try to fire Cook, the first woman of color to sit on the Federal Reserve Board of Governors.

The Trump administration has a new target in its bid to take control of the Federal Reserve and crimp its independence. The big picture: Top housing regulator Bill Pulte is accusing Fed governor Lisa Cook of mortgage fraud.