There likely isn't an option in the game itself, but you can probably disable them from your device.
On Android, you could use Greenify to stop apps from running in the background, which should stop Push Notifications, although it may have side effects if the game requires running in the background. You could also use App Ops and just disable the notification permission if your device is rooted.
On iOS, you can see this question on Ask Different, but basically you go to the app's settings, then Notifications, and then turn them off.