Vet at FirstVet answers:
When cats snore or sound like their nose is blocked they often have a problem within the nose or the region between their nose and soft palate (back of the throat). Examples of conditions that can cause such symptoms include narrow nares (nostrils), common in flat-faced cat breeds; swelling in the nose due to soft tissue inflammation from infections such as cat flu; growths/tumours, etc.
It is not normal for a cat to regularly snore or have abnormal sounds coming from its nose. It is recommended to book an appointment with a veterinarian if this is the case with your cat. X-rays of the airways, samples and examinations of the airways under anaesthesia will likely be required to obtain a diagnosis.