The agency's Baltimore-based field office is leading the bureau's part of the investigation.
Jim Margolin, a spokesman for the F.B.I.'s New York office, which is leading the bureau's investigation, said the agency had consulted with the three men and had done so in the past.
"In his 10 years at the F.B.I., Bob Mueller has set the gold standard for leading the bureau," Mr. Obama said.
Raj Date, who is leading the bureau, said in a statement that student loans can help make lives better by helping people access education.
That measure had been put in place in an effort to prevent directors from amassing the power that J. Edgar Hoover had during his 48-year tenure leading the bureau.
Mr. DeLoach became head of F.B.I. investigations in 1965, leading the bureau's assault on the Klan after the 1964 killings in Mississippi.
It is widely seen as a reaction to the power amassed — and abuses committed — by the founding director of the F.B.I., J. Edgar Hoover, who had died four years earlier after leading the bureau for decades.
"As baby boomers join the ranks of the retired, their hard-earned savings should help them realize opportunities, not serve as the target of deception and fraud," Raj Date, who is leading the bureau, said in the statement.
"The C.F.P.B. needs highly qualified staff, from those who are skilled in handling individual consumer complaints to experts in legislative and intergovernmental affairs to lawyers who are able to craft clear and precise rules," Raj Date, who is leading the bureau, said in a statement.
The FBI director had been leading the bureau's investigation into whether the Trump campaign colluded with Russia to influence the outcome of the 2016 election. .
