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][1] 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][2] and just disable the notification permission if your device is rooted.

On iOS, you can see [this question on Ask Different][3], but basically you go to the app's settings, then *Notifications*, and then turn them off.


  [1]: https://play.google.com/store/apps/details?id=com.oasisfeng.greenify "Greenify on Google Play"
  [2]: https://play.google.com/store/apps/details?id=droidmate.appopsinstaller "App Ops [Root] on Google Play"
  [3]: http://apple.stackexchange.com/questions/28883/how-can-i-turn-off-push-notifications-for-individual-apps-in-ios-5 "How can I turn off push notifications for individual apps in iOS 5? - Ask Different"