The chairman of the Congressional Black Caucus, Rep. Emanuel Cleaver, D-Mo., said if the museum and research center is named to honor Hoover, it should include an asterisk noting his "views on race," USA Today reported.
The museum is scheduled to open in 2013. It said last year it would name the center after Hoover following the acquisition of some 4,000 items he once owned. Among the items is his desk and telephone.
"It is not healthy for the nation if his legacy does not include an asterisk for his (archaic) views on race," Cleaver said. "I'm wondering what Dr. King would say to us."
Hoover's FBI worked to discredit the civil rights leader. Cleaver said the decision to name the FBI headquarters building in the District of Columbia for Hoover in 1972 is still a "sore point for a lot of people."
Former FBI agent William Branon, now the director of the J. Edgar Hoover Foundation, which donated the artifacts, said he "can't think of a more fitting place to carry his name."
He said the decision with museum developers was "in keeping with the goals of the foundation: to perpetuate the good name of Mr. Hoover … no editorializing."
The National Organization of Black Law Enforcement Executives has not opposed naming the museum after Hoover.
"Good, bad or indifferent, that's the history of law enforcement," NOBLE executive director Jessie Lee said.
NOBLE has been a major donor to the museum, the report said.