Greyhounds are no more likely to chase cats than most other dogs, but they are more likely to catch them! If you own a cat the Trust will only offer you 'a potentially cat proof' dog, that is a dog that has been tested in a cat environment to gauge their reaction. Some dogs will never live with cats, some can be trained, some will live with anything. Your homefinder will be able to advise you about the most suitable dog in the kennels.

Greyhounds, like all other dogs still may chase a 'foreign' cat that comes on to their territory, or they may want to chase cats seen on walks. When you introduce the cat and dog for the first time, have the dog on a lead and muzzled.  Don't let the cat attack the dog and keep the dog muzzled until you are confident he/she won't lunge at the cat. It is no hardship for greyhounds to wear a muzzle and it is invaluable as a training aid. A water pistol can also be useful, squirting an offending dog can be very effective. Don't leave them alone together until you trust the dog not to be stimulated by the cat running.

Eventually you can build up to feeding them side by side, and soon they may sleep near each other. You are pretty much home and dry by this time. One word of caution though - it is not advisable to leave the animals in the house together when no humans are there. Not least because cats can attack too, don't assume the dog will be the aggressor.