The agency leasing the Treasure Island space where the barge is being built says the four-story vessel is bound for the Port of Stockton, a destination located about 80 miles east of San Francisco.
The Treasure Island Development Authority says it has been notified the barge will move by March 7.
Google Inc. and the Port of Stockton didn't immediately respond to requests for comment.
The barge is leaving because of a Jan. 31 regulatory order concluding that Google didn't have the proper building permits at Treasure Island.
Google says the barge will become a floating technology center once it's done.
Stockton Police have increased street patrols in several neighborhoods in Stockton after a wave of gun violence during Memorial Day weekend.
The Stockton City Council has voted to reduce the salaries of the mayor and city council by 30 percent. The discussion about the salary cut during Tuesday night's city council meeting was a heated one.
A national museum to highlight Filipino history in America is planned to open in October in Stockton. At one time more Filipinos lived here than anywhere else in the nation.