The idea to prohibit drinking surfaced after several complaints about drunk people at the Encinitas Community Park.
Sheriffs deputies have been called to the park eight times, and investigators say they have arrested one man for public intoxication since January.
After hours of discussion, the City Council voted unanimously to take another hard look at the proposal before acting.
City staff members will now attempt to determine if there is a systemic problem with drinking at the parks.
The next City Council meeting about possible park prohibition has not been announced.