Most greyhounds are fine with cats. Be sure the adoption agency knows you have cats. They will be happy to introduce you to cat-friendly dogs. As a precaution, the greyhound should be muzzled for the first few days he's home. Once he realizes the cats are part of the family, there should be no trouble.
Many greyhounds are actually afraid of cats.
Greyhounds and muzzles . When you see greyhounds together at the track, they are always muzzled. There are a couple of reasons for this. When they are actually running, they are very competitive and will sometimes nip at another dog's neck. With their thin skin, this can run up vet bills.