Durant has apologized for threatening and profane comments he made to entertainer Michael Rapaport through social media.
Rapaport released images of the private messages Tuesday on his Twitter account, and they included homophobic and misogynistic language from the Brooklyn Nets star.
Brooklyn coach Steve Nash said the team has discussed the remarks but would keep the conversation internal.
Durant is nearing a return from a left hamstring strain that has sidelined him since mid-February. He could be back sometime next week.