CNN said it spoke with 16 people as part of its investigation into the 80-year-old actor, some of whom also alleged inappropriate behaviour by Freeman at his production company, Revelations Entertainment.
In a statement, Freeman said he was sorry to anyone who had been made to feel uncomfortable or disrespected.
"Anyone who knows me or has worked with me knows I am not someone who would intentionally offend or knowingly make anyone feel uneasy," the statement said. "I apologize to anyone who felt uncomfortable or disrespected -- that was never my intent."
Representatives for Freeman and Revelations Entertainment did not respond to requests for further comment. Reuters was unable to independently confirm any of the allegations.
Multiple accusations of sexual misconduct against male actors, filmmakers and agents have roiled Hollywood since October 2017, leading in some cases to resignations and the halting of projects.
Similar accusations have also engulfed men in US politics and business, and inspired a #MeToo social media movement by victims sharing their stories of sexual harassment or abuse.
CNN said eight people told the network they were victims of what some labelled harassment and others called inappropriate behaviour by Freeman. It said eight others told the network they witnessed the actor's alleged misconduct.
CNN also said other sources denied having seen any questionable behaviour by the actor, and that those sources described him as being professional on set and in the office.
Freeman, whose career has spanned 50 years and more than 100 movies, won an Oscar in 2005 as best supporting actor for his role as a former boxer in "Million Dollar Baby."
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