The gurgling sound in a sink drain is an air-related issue. SF Gate says that either the drain has no vent, it has an improperly installed vent or a vent is blocked. This issue creates a vacuum as water passes through the drain that makes a sucking noise as the pressure equalizes in the pipes.
If the drain has a vent, owners should be able to locate it on the roof near the location of the offending fixture. If the roof is accessible, the vent is easy to inspect. Birds and other small animals often build nests in vents, blocking access to air. Cleaning the debris from the pipe allows the air necessary to equalize pressure. If the materials are not accessible from the top of the pipe, a plumber's snake or water hose can help to move them through the vent and wash them down the drain.
When snow and ice accumulate on the roof of a home, they also have the potential to block vents. Removing the accumulations stops the gurgling drain. However, under these conditions, it is essential that the individual use caution as the roof is extremely slick. It is often a better option to allow nature to thaw the ice, even though it involves listening to the gurgle each time someone uses the drain.