Ballmer, 58, signed a deal to buy the Clippers for $2 billion in late May with Sterling's wife, Shelly, but Donald Sterling has been challenging his wife's authority to sell the team in state court.
Ballmer and Donald Sterling had a "friendly conversation" on Monday, sources told Shelburne.
Commissioner Adam Silver said last week he wasn't sure if a new owner of the Clippers would be in place before the start of next season.
Writes Shelburne: "The original agreement called for the sale to close by July 15, with a possible extension to Aug. 15. The NBA has the option of resuming termination proceedings and subsequently selling the team itself if the sale is still in limbo by Sept. 15."
Shelly Sterling is set to testify in the civil case between her and her husband on Tuesday.
- Chris Mascaro