Fila's have basically the same predatory motor patterns as a Rottweiler. You can desensitize a dog with the full series of motor patterns to your own cat...it takes awhile (I did it out of desperation with my Rottweiler who had exceptionally intense eye stalk towards smaller dogs, cats etc.). When a dog with the enhanced motor patterns is desensitized to your cats they normally will be very good with "their" cats. The action that triggers chase motor pattern is quick movement, I was lucky I have a cat that "knew" she was being stalked and froze. I also made sure I had places for my cat to go where my Rottie could never follow her if she needed an escape route...but, when I first brought my Rottie home (she was almost a year) I did not let them meet for about 2 months and let my Rottie get used to her scent. Then the cat started coming up to the baby gate I had sectioned off the living room for the cat...when my Rottie finally stopped lunging and going crazy when she saw the cat, the cat started laying by the baby gate and my Rottie would lay on the other side quite comfortable with the cat...it was then I let the gate down. They have been perfect friends ever since. Of course, this doesn't mean I trust her with "all" cats...I don't even trust her with our own cat outside...if the cat runs the eye stalk and chase motor pattern naturally kick in.
The predatory motor patterns start with eye stalk, going to chase, to grab bite then kill bite and dissect (maul)...the worst thing with an improperly socialized dog with the full series of motor patterns is you have to be very careful as once they show eye stalk, then chase the other motor patterns naturally follow suit...only dogs that have some of their motor patterns deselected by selective breeding (for instance a retriever) has only chase-grab-bite....no kill bite and no dissect.
The only way to help this dog is to either refer the dog to the rescue center...or if you take the dog be prepared to make safe havens for your cats and to get professional help. You can also teach a dog with high prey drive an emergency down...if the dog will listen
you have better luck getting a dog in eye stalk motor pattern to down than you would ever have of the dog coming back to you...the dog can still see the prey object when in down position...I have had small success teaching down to my Rottweiler in times of eye stalk, the secret (for my dog anyway) is to catch her before she goes into chase motor pattern.
I still have to be very careful with my Rottweiler, small dogs, quick moving animals etc are prey for her. I always have to keep her on a leash unless I know the area I am hiking has no other dogs or children. It can be very hard to deal with, and prey drives are not aggression, they are a natural part of a dog...something man selected for and enhanced the drives for these sought after motor patterns...perfected for their jobs they had to do. Dogs with the full series of motor patterns do not need to be taught how to hunt, it's natural and bred into them by years of artificial selection. It's up to you if you want to take on this challenge...I did and I am glad I did, and it makes me proud when I can tell the animal behaviorist (who I was working with and who told me with her predatory drive I would NEVER get her around small animals especially a cat)...it made me very proud of how much I accomplished with her and makes me realize that as long as you understand what you are dealing with and how the motor patterns work...then you will be prepared and will never place your dog in a situation where they have to prove them selves without being desensitized to the situation first.