Adult film and magazine company Hustler has issued a statement claiming to have a copy of such a recording.
"Hustler are in possession of the Rihanna and J-Cole tape," it said. "We have seen it and we do not know what we are going to do with it yet."
Rihanna responded on Twitter: "We don't believe U, U need more people...AND ofcourse an actual sextape! #slownewsday."
The 'What's My Name' singer has said that she was "humiliated" and "mortified" when she first heard that naked photographs of herself had leaked online.
However, she also admitted that she may take more nude shots of herself, explaining: "When you're alone, and those horny moments come up, pictures can be very handy."
> Rihanna 'would consider posing nude'
> Rihanna 'poses topless for magazine shoot
> Rihanna: 'Everyone should do nude pics'
Watch the Rihanna 'Only Girl in the World' video below: