Perfect Rhymes:
* Roar: This is a sound animals make, not a specific animal.
* Shore: Not an animal itself, but related to the ocean where many animals live.
Near Rhymes:
* Door: This doesn't rhyme perfectly, but it's close enough to be considered a near rhyme.
* Boar: A wild pig, which is an animal.
* Pour: Not an animal, but can be used to describe the action of an animal drinking.
Let me know if you'd like to explore other possibilities!