CNBC staffer Ylan Mui reports that the White House is considering Brian Brooks, a top official at Fannie Mae, to head the Consumer Financial Protection Bureau, according to two people familiar with the discussion.

Brooks has close ties to Treasury secretary nominee Steven Mnuchin and represented several of the investors in Mnuchin's purchase of failed subprime mortgage lender IndyMac for $1.6 billion in 2009. The bank was renamed OneWest, and Brooks joined the company as vice chairman.

The term of the current CFPB director, Richard Cordray, does not end until 2018, though opponents of the agency are pushing to have him removed earlier.

Though the director is a political appointee, the CFPB is an independent agency — which means the White House has limited authority to make changes at the top. Currently, the president can fire the director only for inefficiency, neglect of duty or malfeasance.

But a recent ruling by the D.C. Circuit Court found that the agency's structure is unconstitutional. (The CFPB is appealing that decision.) Meanwhile, Republican Rep. Jeb Hensarling of Texas is expected to propose legislation soon that would allow the president to dismiss the director of the CFPB for any reason, according to a memo obtained by CNBC.

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