The whale is an easter egg found in the GameCube titles while traveling to the Island on Kapp'n's boat. The whale cannot be caught and is rarely seen. In Animal Forest+ and Animal Crossing, there is between a 1% and 4% chance of seeing it on any given trip depending on the month. The greatest chance of encountering it is during January and February. In Animal Forest e+, the chances are never greater than 1% due to the increased number of ocean fish.
If the player uses external devices or glitches to walk on water, they can encounter the whale and attempt to catch it to no avail. This is because fish do not bite in the open ocean. Assuming the whale could be caught, it would likely lead to the game crashing as it has no fish data associated with it.
The game's code confirms it is a whale, as its associated data is called whale_data.