According to TMZ, the argument took place on April 9, after Sterling's girlfriend, V. Stiviano, posted a photograph on Instagram of her posing with NBA legend Magic Johnson. On the tape, Sterling also told Stiviano not to bring Johnson to games.
"You can sleep with [black people]," Sterline says on the tape. "You can bring them in, you can do whatever you want. The little I ask you is not to promote it on that ... and not to bring them to my games."
"It bothers me a lot that you want to broadcast that you’re associating with black people," Sterling also says. "Do you have to?"
In the recording, Stiviano says she herself is "black and Mexican... whether you like it or not."
According to TMZ, Sterling has previously been sued by former Clippers executive Elgin Baylor for racial discrimination, although the suit was unsuccessful.
In response to the audio tape, Johnson told TMZ it was "a shame that Donald Sterling feels that way about African-Americans."
"He has a team full of amazing African-American basketball players that are working to bring a championship to Clippers fans," Johnson said. "The Clippers also have a strong minority fan base."
You can listen to the tape here.