Cats can indeed purr while they sleep. Research and veterinary guidance indicate that purring during sleep is a common occurrence, especially during lighter sleep stages, and can be related to relaxation, contentment, or dreaming activity. Purring during deeper sleep or REM sleep may decrease or pause, just as other sleep behaviors change across sleep stages. The exact frequency of purring noises can vary by individual cat and situation, but it is a recognized nighttime behavior in many felines. If a cat purrs while sleeping, it is typically not a sign of distress, though unusual breathing, snoring, coughing, or changes in sleep patterns could warrant a closer look from a veterinarian.