If your faucet has an air gap, the sound you hear is completely normal. Air-gap faucets are required by plumbing codes in many areas, and the noise is simply part of how they operate.
Another common cause happens when your drinking water system is installed under the sink. If you hear a gurgling sound, it’s usually the system discharging rejected water down the drain while it’s producing purified water. This noise should only occur right after you use the system and will stop once the storage tank is refilled.