When rehoming a pet, what's a polite way to say "no thank you, we're not interested in giving you our pets"?

Tell people up front that you have many people who are interested and you are screening applicants and will let them know if they have been picked by a certain date. They are your cats and you have the right to give them to the right home. If it makes you feel more comfortable you may ask or go see the potential living quarters.