The ex-football player and occasional actor, who is now serving time in Nevada for armed robbery and kidnapping, has always denied he killed the pair.
The Washington Post reported Winfrey told people gathered at the National Cable & Telecommunications Association convention in Chicago she wants Simpson, who turns 64 next month, to submit to an interview for her Oprah Winfrey Network and admit killing his ex-wife and Goldman.
"I have a dream of O.J. Simpson confessing to me," the Post quoted Winfrey as saying. "And I am going to make that happen, people. I don't just want the interview. I want the interview on the condition that you are ready, Mr. Simpson."
Celebrity Families of 2014 [PHOTOS]