It is safe to keep sunflowers if you have a cat at home. Sunflowers can be grown together with cats, and the roots, stems, and leaves of sunflowers will not cause poisoning to cats.
What can't you keep as a cat at home?
1. Daffodils. Daffodils can severely irritate a cat's stomach and intestines, and ingestion can seriously affect a cat's health.
2. Dieffenbachia (Dumb Cane). The fruit is poisonous; ingestion can cause swelling and pain in the mouth and throat, and can seriously endanger a cat's life.
3. Lilies. Cats can suffer kidney failure if they smell lily pollen. Accidental biting can severely damage their kidneys.
4. Chrysanthemum. If a cat accidentally ingests chrysanthemum, it may experience loss of appetite, vomiting, diarrhea, and depression. 
5. Tulips. Tulips are bad for a cat's stomach and can cause vomiting and diarrhea.
6. Alocasia macrorrhiza (also known as Dieffenbachia). Its highly toxic stems and leaves can cause blindness in cats. Ingestion can even lead to cardiac arrest and death in cats.
7. Cyclamen. If ingested, it can cause cats to vomit violently and may even lead to allergic reactions and death.
8. Azaleas. They can cause gastrointestinal upset, central nervous system disorders, low blood pressure, coma, and death in cats.
9. Hydrangea flowers. If a cat eats them, it can cause symptoms such as stomach pain and weakness.
