Cooley spokesman Kevin Spillane said Thursday that there aren't enough outstanding votes for Cooley to overtake Harris.
Spillane said Cooley called Harris Thursday morning to congratulate her. Still the San Francisco district attorney is not counting the race as over.
"The counties continue to tabulate votes, and District Attorney Harris believes it is only appropriate to wait until all the votes are counted before making a public declaration," Brian Brokaw, Harris' campaign manager, said.
Harris will hold an event next Tuesday, the day all counties are required to report their final counts to the California Secretary of State.
The San Francisco district attorney would become the first woman and first minority elected as California's top law enforcement official. She would replaced Democrat Jerry Brown, who gave up the office in his successful bid for governor.
Harris is up by 51,000 votes, a half-percentage point margin, with 150,000 votes still uncounted.