You have likely noticed when your cat is in a deep sleep, twitching occurs. You can see the mouth, whiskers, legs, and even tail moving. Some cats will even purr or make quiet meowing or hunting sounds. So the short answer is yes, cats do dream. There is evidence behind this.
Humans have 5 stages of sleep; REM (rapid eye moment) sleep being the 5th stage where dreams occur. We spend about 20% of our sleep in the REM stage, with babies spending 80% of their sleep in REM. In cats, about 30% of time spent sleeping is in REM sleep, though they sleep double the average adult human each day. Cats display different movements, much like humans, that indicate they are dreaming. They twitch, move whiskers, wiggle their tail, extend and retract claws, shake paws, move their lip, and even make cat sounds while sleeping. Cats emit substance from the brain to refrain them from vividly acting out what is happening in their dream, just like our brains do.
When cats make a low chirping sound, referred to as “chattering”, they are verbally telling they have found prey. Many indoor cats do this while humans or other cats are nearby as a signal. In a REM staged dream, cats will actually make this chirping sound which indicates they are dreaming of some form of prey, possibly remembering something they have hunted before.
Because cats sleep around 16 to 18 hours each day, it is very easy to catch them in a REM sleep. Simply observing their movements, you can almost pinpoint what they are dreaming about based on their personality, movements, and sounds they make.