The man is identified by the publication as investment banker James Montgomery, CEO of Montgomery & Company.
The footage -- purportedly shot at a 2004 fundraiser for St. Matthew's Parish School, a private day school in Pacific Palisades, California -- shows a white man dressed up in an African tribal outfit and black makeup. He carries a stuffed chimpanzee and wears a wig.
At one point in the video, Hanks jokes, "Ladies and gentlemen, a celebrity in our midst. Who would have thought that Bill O’Reilly would join us?”
Frey adds, “All I know is, this school is so conservative that Jamie Montgomery was almost not allowed in."
Also read: Hollywood Won't Learn: It's a White Summer Again 
"Our policy is not to comment on past or current parents," Stuart Work, the head of St. Matthew's, told TheWrap.
The fundraiser was reportedly centered on a "Castaway" theme -- a reference to the 2000 hit film starring Hanks.
The Daily Caller was co-founded by political analyst Tucker Carlson and launched in 2010.
Montgomery and a spokeswoman for Hanks did not immediately respond to requests for comment.