Geffen said he and Ellison would run the team, while Winfrey would be an investor.
"Oprah is not interested in running the team," Geffen told Schaap. "She thinks it would be a great thing for an important black American to own [another] franchise.
"The team deserves a better group of owners who want to win. Larry would sooner die than fail. I would sooner die than fail. Larry's a sportsman. We've talked about this for a long time. Between the three of us, we have a good shot."
Winfrey's spokesperson, Nicole Nichols, issued a statement later Wednesday, confirming Geffen's claim.
"Oprah Winfrey is in discussions with David Geffen and Larry Ellison to make a bid for the Los Angeles Clippers should the team become available," Nichols said in the statement.
Geffen, a music and film mogul with a net worth that Forbes estimates at $6.2 billion, reportedly tried to buy at least a controlling stake in the Clippers in 2010 for $600 million but was rebuffed by Sterling.
Geffen also told Schaap that LeBron James was interested in playing in Los Angeles when he was a free agent in 2010 and that James, who ultimately signed with the Miami Heat, told him he would not play for Sterling.
"[The] reasons are perfectly clear," said Geffen, would not specifically disclose why James didn't want to play for Sterling.
"I'm a fan. I bring something to the table, it's fun and I can afford it," Geffen said. "I live in L.A., that's one thing that makes it attractive."
Geffen said he and Ellison, the CEO of Oracle, a business software and technology company, were also interested in buying the Los Angeles Lakers, but the team wasn't for sale.
NBA commissioner Adam Silver wants Sterling to sell the Clippers as part of the extremely stiff sanctions brought against the longtime owner in response to racist comments the league determined he made in a recorded conversation.
Silver banned Sterling for life, fined him $2.5 million and said he will press the other teams to support his desire to make Sterling sell.
"I fully expect to get the support I need from the other NBA owners to remove him," Silver said.
Silver was asked Tuesday whether the league was considering more minority ownership in response to the sanctions against Sterling.
"As you know, we have an African-American primary owner in the league right now," Silver said. "Shaquille O'Neal just became a small owner of the Sacramento Kings. David Robinson is an owner of the San Antonio Spurs. Vivek Ranadive, a person of color born in Mumbai, India, just became the primary owner of the Sacramento Kings. So I believe we have a very diverse league, but I'd always like to see it become more diverse."
Boxing superstar Floyd Mayweather Jr. and music mogul Sean Combs both claimed interest in buying the team Tuesday, as did real-estate tycoon Rick Caruso.
Magic Johnson, Mark Walter and their Guggenheim Partners group, which made the billion-dollar purchase of the Los Angeles Dodgers in 2012, also are possible bidders, though sources have told ESPN that any such discussions were premature at best.
Johnson, who was specifically mentioned in the recorded conversation involving Sterling, laughed off the suggestion he should buy the Clippers in an appearance on ESPN on Sunday night, saying he was focused on bringing the NFL back to Los Angeles.
ESPN's Jeremy Schaap, ESPN.com's Dan Rafael and The Associated Press contributed to this report.
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