Mr. Mulvaney made a series of recommendations to lawmakers that would curb the bureau’s power and independence. He called for it to be funded through congressional appropriations, rather than through the Federal Reserve, which has insulated it from political jockeying. He also recommended that bureau rules be subject to legislative approval and advised that the president should have direct oversight and authority over the bureau’s director. Right now, the director can be removed by the president only for specific and justifiable cause, rather than for political or other reasons.

Mr. Mulvaney also recommended the creation of an inspector general’s office to monitor the activities of the bureau.

“By structuring the bureau the way it has, Congress established an agency primed to ignore due process and abandon the rule of law in favor of bureaucratic fiat and administrative absolutism,” Mr. Mulvaney said.

Republican lawmakers have tried for years — without success — to curb the powers of the agency, which was authorized in 2010 and enjoys broad support among congressional Democrats.

While Mr. Mulvaney — or the person that Mr. Trump eventually selects to succeed him — can weaken enforcement efforts, the fixes that he called for would require legislation. The chances of this are slim, as Democrats in the Senate have vowed to block any bills that would harm the consumer bureau.