President Trump is considering naming Mick Mulvaney, director of the Office of Management and Budget, to run the Consumer Financial Protection Bureau on an interim basis, potentially setting up the watchdog agency for a massive overhaul, according to a person briefed on the planning.

Mulvaney, who once called the CFPB a “joke,” would replace Richard Cordray, one of the few remaining Obama-era banking regulators, who announced Wednesday that he plans to step down as the agency’s director by the end of the month.

If given the job, Mulvaney would probably lead both agencies until a permanent head of CFPB is chosen and confirmed by the Senate, said the person, who was not authorized to speak publicly about the matter. The offices of the OMB and the CFPB are across the street from each other in Washington.

Cordray’s resignation gives Republicans an opportunity to remake an agency they have long complained is too powerful. Republicans had become increasingly exasperated that Cordray, whose term does not end until next summer, had not stepped aside when Trump took office and instead continued to press for aggressive rules disliked by the business community.

The CFPB director can be fired only for cause, and the agency gets its money from the Federal Reserve rather than Congress, giving it an element of independence that Republicans have complained it has abused.

Raj Shah, the White House principal deputy press secretary, said, “The administration will announce an acting director and the president’s choice to replace Mr. Cordray at the appropriate time.”

In a 2014 video interview with the Credit Union Times, Mulvaney, then a congressman, complained that it could sometimes be difficult even to have the CFPB return a phone call. “It has been a truly adversarial relationship. The CFPB, by virtue of the fact that they don’t need Congress to exist,” is difficult to hold accountable, he said. “The place is a wonderful example of how a bureaucracy will function if it has no accountability to anybody.”

The agency is a “joke . . . in a sick, sad way,” he said.

The looming transformation of the CFPB could be significant. The agency was one of the central achievements of the Obama administration after the 2008 financial crisis. Created under the 2010 financial reform bill known as Dodd-Frank, it regulates the way that banks and other financial companies interact with consumers, policing payday loans and mortgages, among other things. The CFPB has extracted billions in fines from big banks, including $100 million from Wells Fargo last year for opening millions of sham accounts that customers didn’t ask for.

Under new Republican leadership, the agency is likely to focus less on writing new rules for the financial industry or extracting big fines, industry experts say. The CFPB has been working on rules concerning debt collectors and bank overdraft fees, for example, but those efforts are likely to stall under the new leadership, industry officials said.