The City Council is scheduled to discuss the plan by Councilwomen Desley Brooks and Nancy Nadel at their meeting on Tuesday and could vote on it.
The proposal would restrict funding the police and city attorney's office need for the injunctions.
One injunction is already in place. Oakland City Attorney John Russo is seeking another and has made plans to pursue still a third.
The injunctions restrict the movement of alleged gang members. Supporters say they are another tool to keep neighborhoods safe.
Critics say they are a form of racial profiling.
Oakland Mayor Jean Quan has said money for the injunctions could be better spent on social programs.