The report was published by Tribune, citing two unnamed federal officials. NBC News could not immediately confirm the report.
"It was sex," one of the sources said, according to Tribune.
One official told Tribune that the alleged misconduct dates to Hastert's time as a high school teacher and wrestling coach in Illinois.
The school district where Hastert taught and coached wrestling from 1965 to 1981said Friday that it had "no knowledge of Mr. Hastert's alleged misconduct, nor has any individual contacted the District to report any such misconduct."
Hastert was indicted Thursday on charges that he structured bank withdrawals to avoid federal reporting requirements and later lied about it to the FBI.
The indictment said that Hastert was paying an unidentified person from his past to conceal Hastert's "prior misconduct." The indictment did not specify the alleged misconduct or name the person.
Representatives for Hastert have not returned requests for comment from NBC News.
Charles Hastert, a nephew, told NBC News on Friday that his uncle "has always been as honest and clean as they come." He said he believes the charges are probably a political witch-hunt.
Jeff Jerabek, who was on the wrestling team in the mid-1970s, said there was never so much as a rumor of impropriety. He described Hastert as friendly and in tune with his students.
"If you had a problem, it wouldn't be hard to talk to him about it," said Jerabek, whose two older brothers were also on the team. "I remember one time I was walking along with a frown and he said, 'Hey smiley, cheer up.' Some teachers, it's just a job. Not him. He was a friendly guy."