The Los Angeles Police Department and State Department of Justice are just two of the agencies expressing reservations. Information would be stored on Google servers instead of city computers.
The plan was already approved by the City Council's Information Technology and General Services Committee and is currently before the Budget and Finance Committee.
General manager of the city's Information Technology Agency, Randi Levin, estimates the Google-based system would save $8 million to $30 million of taxpayer money.
"The ability to get whatever information the city needs, when they need it, on whatever device they need it on, and to collaborate on all sorts of documents would fundamentally change the way the city works and enhance productivity greatly," she said.
City officials say Google is addressing security concerns by making sure data is stored in dedicated facilities within the United States and is managed by staff with high-level security clearances. The contract could reach the full city council for a vote within a few weeks.
CNS contributed to this report.