Whales are only visible once Fishing is researched.
Originally, each whale would require resources to hunt before receiving the 10 star reward. This cost increased with each subsequent settlement and could result in the cost of hunting whale to outweigh the 10 resource reward. This was removed in a later update, and hunting each whale now has no cost associated with it.
Midjiwan, the game developer, officially does not recommend hunting actual whales.
Whales can occasionally spawn on shallow water tiles, although this is quite rare.