Last Updated May 29, 2015 10:59 PM EDT
Former U.S. House Speaker Dennis Hastert allegedly agreed to pay millions of dollars in "hush money" to conceal accusations of sexual misconduct in his past, two law enforcement officials told CBS News.
Law enforcement sources say the misconduct mentioned in court documents refers to sexual misconduct dating back more than 30 years. From 1965-1981, Hastert was a popular teacher and wrestling coach in Yorkville, Illinois.
Late Friday, a federal law enforcement source told CBS News Justice and Homeland Security Correspondent Jeff Pegues that the allegations involved a former male student.
The source said the FBI investigation -- which was led and "tightly held" by the FBI's Chicago field office -- did not delve into the sexual misconduct allegations. When asked if Hastert has cooperated with investigators, the source told Pegues that the former speaker "still hasn't come clean."
Hastert was indicted and charged Thursday with violating federal banking laws and lying to FBI investigators. According to the indictment, Hastert agreed to pay $3.5 million in 2010 to a person identified only as "Individual A," in an effort to "compensate and conceal" Hastert's "prior misconduct."
The indictment did not reveal details of the misconduct, but it did note that Hastert and Individual A have known each other for "most of Individual A's life" and that the individual is from the same Illinois town where Hastert was a teacher and coach.
Hastert's former employer, the Yorkville School District, said in a statement Friday that it was "first made aware of any concerns regarding Mr. Hastert when the federal indictment was released on May 28, 2015."
The school district "has no knowledge of Mr. Hastert's alleged misconduct, nor has any individual contacted the District to report any such misconduct," the statement explained. "If requested to do so, the District plans to cooperate fully with the U.S. Attorney's investigation into this matter."
Legal analysts have said it's unlikely the details about Hastert's former job would have been included in the indictment if they didn't play some kind of central role in the controversy. "Notice the teacher and coach language," Jeff Cramer, a former federal prosecutor, told the Associated Press. "Feds don't put in language like that unless it's relevant."
To keep the controversy private, prosecutors allege that Hastert withdrew a total of $1.7 million from a number of his personal bank accounts to give to Individual A over a four-year period.
According to the indictment, at first, he took out large amounts -- "$50,000 withdrawals of cash" on 15 occasions. But when "bank representatives questioned" him in 2012, "Hastert began withdrawing cash in increments of less than $10,000" because banks are required by federal law to report anything larger.
In 2014 the FBI questioned Hastert about his withdrawals, and he allegedly lied, telling agents "I kept the cash. That's what I'm doing." He suggested he did not trust the banking system.
Hastert is the longest-serving Republican House Speaker in history, and the job put him in line for the presidency after the vice president.
It was his clean image that led Republicans to tap him as speaker in 1999, during a turbulent period for the GOP. Newt Gingrich had been ousted from leadership over an ethics violation, and the man who was to set to replace him as speaker, Bob Livingston, admitted to an extra-marital affair.
"They turned to Denny Hastert because he was the affable, easy to get along guy," explained Washington Post congressional reporter Paul Kane. "This has shocked Democrats, Republicans, lobbyists, consultants really everybody, it's really rocked this town."
Hastert also resigned Friday from the board of directors of a center bearing his name at Wheaton College.
"Wheaton College has received and accepted the resignation of Wheaton alumnus and former Speaker of the U.S. House of Representatives J. Dennis Hastert from the Board of Advisors of its J. Dennis Hastert Center for Economics, Government, and Public Policy," Wheaton, a Christian college in Illinois, announced in a statement. "The College respects Mr. Hastert's distinguished public service record and the due process being afforded him pursuant to the charges that have been filed against him."
CBS News Homeland Security Correspondent Jeff Pegues contributed to this report.