This isn’t a simple black and white question and we uncovered different considerations, some of which I’ll discuss for you here.

Choosing a breed to keep a cat content is not just about the breed but also can be a dogs temperament, age, a cats feelings, a cats experience and home interior.

My first consideration would always be what the cat does when they see a dog. Are they petrified? If so this isn’t conducive for living with a dog. Cats can experience stress related behaviours which can include urine infections. They can spray urine or midden (poo in places) as they are scared.

A greyhound has an inherent desire to chase therefore they wouldn’t be suited to living with cat.

Does your cat have places to relax and eat and not have their litter tray ambushed? Do you have a space for this?  

Can they go somewhere high and can they climb or do they have health issues? Can they go outside? An indoor cat may find a dog coming into their home very stressful.

Asking if the puppy/dog has been used to living with cats (and enjoys it!) and therefore habituated to them is important.

The lady I spoke to is going to see her cats reaction to another dog in her garden. The dog will be on the lead and the cat can go inside at any time. It can perch on the table and she will monitor her reaction before making any decisions.