"Doc is troubled by this maybe moreso than anybody else," Parsons said. "If Mr. Sterling continues as owner, he does not want to continue as coach."
Parsons is testifying at a trial that could resolve whether Sterling's wife, Shelly, can complete a $2 billion sale of the Clippers to former Microsoft CEO Steve Ballmer.
NBA commissioner Adam Silver issued a lifetime ban and $2.5 million fine to Donald Sterling in April after he was recorded making racist remarks.
Rivers, 52, led the Clippers to a 57-25 record and the No. 3 seed in the Western Conference last season before falling to the Thunder in the second round of the playoffs.
- Chris Johnson