My guess is he won't do anything more than he does now. My 2 Danes love harrassing the 2 cats. Usually the cats can get away from them pretty easily. However every once in a while, a dog will get a cat cornered. When that happens the dog will walk up to the cat, touch him with his nose then let him go. It's like he is saying "gotcha this time" :smile:
Often the dogs will charge a cat just to watch them run, I think. :Smile:
They are all alone in the house together often. I've never seen any blood on the carpet or walls anytime except the time the cats killed a rabbit inside. :smile:
You're going to have to judge for yourself about your dog and cat depending on the behavior you observe.
Let's liven things up again with a wee bit of friendly disagreement.

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You cannot compare your Danes with Rann’s dog, Raw; I don't think you have too much to worry about with your Danes, either. But all 3 breeds Rann mentioned - Corgi/Heeler/Dachshund – are extremely high prey drive.
It’s
possible that the activity will never escalate. But the fact that Rann's dog becomes “fixated” on the cat should send up warning flags. If it were
my cat (and my dog), I wouldn't leave it to chance...
Unfortunately, it's often a natural progression for the chasing/herding behavior of otherwise “sweet dogs” to turn more serious - especially when it comes to small "prey" animals such as cats, rabbits, squirrels etc.
Over the years, we’ve seen this happen many times, with many dogs. And at the risk of sounding melodramatic, once the dog has a “taste for blood”, it’s a very hard behavior to overcome ...
A typical example is that of a friend’s Standard Poodle. He was a sweet, mild-mannered dog who happened to enjoy chasing squirrels. We often heard that,
“He would never actually hurt one; he's just playing.” ... that was until one day the dog finally managed to corner a squirrel. With no recourse, the squirrel attacked, and was quickly dispatched. After that, this sweet Poodle became an expert squirrel killer.
Without having all the details, from what I've read, I would consider supervising some ongoing bonding between the dog and cat. This is one of those (rare) instances where I would use treats ... lots of treats!
I’d go into more details, but I think you get the idea. And I’ve already given Raw enough here to tear apart.

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Enjoy and good luck!