Venus and Serena Williams have said they will never play at the venue again.
They were jeered by the Indian Wells crowd when Venus withdrew from a match against Serena in 2001.
Their father has claimed they also were the objects of racial slurs.
"I can guarantee you the chances of getting me to Indian Wells are slim to none," Serena Williams told the Los Angeles Times. "I have no interest in going. It's just how I feel. And I think anyone that went through what I went through would feel a similar position."
Larry Scott, the tour's chief executive, has said there will be no exceptions for appearances at Indian Wells.
He plans to discuss the matter with the family next week, the newspaper said.