The Green Eyes of Bast by Sax Rohmer

Psychic investigator Dr. Damar Greefe is strolling home. It's been a tough day, assisting the police. During this stroll, he feels someone or something watching him -- but when he turns to see who it is, he faces only emptiness. Then he sees a cat staring at him, eyes as green as jade. But when he goes to investigate, the cat has disappears!