So many people hunt their reserves/maps without knowing if they have a Great One on the map. I think something that'd be cool would be an alert sent to your phone, like a mission alert in game when you load in from the Warden with something to the effect of "There's been reports of a magnificent animal on the reserve lately, see if you can track him down"
No context or clues as to where it is, what it is (if hunting somewhere like Layton with multiple Great Ones) or anything else.
It would just give us a tip that it's somewhere, and then we either can then focus our efforts on hunting them, or at least know not to start a multiplayer game potentially losing the trophy to another player.