For our dog's ancestors, predation was their form of survival. Dogs nowadays through their genes can still have that drive to want to hunt for survival. haThey have no control over this behaviour. Predation is through genetics. Your dog will not grow out of it.
The Predatory Sequence
Orientation >> Stalk >> Creep >> Chase >> Grab-bite >> Kill-bite >> Possess >> Dissect >> Consume
** it must be noted that this isn't the sequence for every dog. A Border Collie for example stops the sequence at chase because we wouldn't want a working sheepdog to be grabbing and killing livestock. Some dogs may also miss out some of the sequence steps, such as with a Spaniel, you may see orientation and then straight to chase then grab-bite.
How can we deal with predatory behaviour?
> Implenting management and training techniques on our daily walks to help keep our dog calmer and more focussed on their guardian. This could be using a long line to stop the rehearsal of our dog running off to hunt on their own.
> Learning to perform the safe parts of our dogs predatory sequence with predation substitute tools
> Creating outlets for our dogs using predation games to help meet their hunting needs
> Introducing a safety cue that immediately interrupts unwanted predatory chasing
Every dog has innate needs that they need to fulfil. Say your dog sees a deer, their need could be to chase the deer because it represents food and survival. Now we could recall our dog away from the deer and get the dog to run back to you instead. The dog is still getting the chase aspect but they may not be getting the innate need of you giving them a treat being a substitute for the 'prey'.
This would mean the behaviour of running up to you as you've recalled them isn't functional. Again, they may get the chase aspect from the recall but if your dog is wanting to hunt: chase, bite and kill... then the chase part isn't enough of an outlet for them.
Have a think about your dog's predatory sequence... are you giving them enough of an outlet?
What could you be offering them that mimics parts of their predatory sequence that they absolutely love to perform?