Having a Spyglass is a Must as it stops you from potential getting mauled (by the cat you're looking at at least).

From there, if it has a Green Icon above it's head, then you're go to go passive feed it some prime meat and the Cat distribution will work as instead.

If its Yellow or Red icon, it will try to attack you, hope you're near some water and jump in.

If it says "this cat doesn't want to be tamed by you" try a different Cat