My dog will bring balls and frisbees to my cats in hopes of playing fetch. Even if they could, they aren't interested. He also REALLY likes to lay near them. I don't know if he is just obsessed with staring at them or if he genuinely wants to snuggle but they don't like that either. I also had to install a cat door into the basement to keep the cat box safe.
The cats were really scared of the dog at first even though they were two times his size. I think it would have been easier to introduce them if the cats were younger. They are set in their ways. I doubt I'll ever see the cats snuggling up to Toby but in just a few months they have improved so much. They won't get out of the bed if he lays near them (just give him major stink eye) and they don't run away if he is in the room. He does like to run up on them but we don't let him. I'm hoping with consistent redirecting he will eventually get past it.