Are strawberry PLANTS parrot safe?

Our parrot has a play-tree right by a very sunny window. I would like to grow some strawberries indoors, and the pot would need to sit by his stand (due to space restrictions). He wouldn't be able to reach the dirt or pot, but if they grow well, he may be able to reach some of the leaves. I grow several kinds of pepper plants by his cage, and he never seems to bother anything but the peppers on those, so I would assume he probably wouldn't bother the foliage on the strawberry plants either. But just in case, I'd rather be safe than sorry. Does anyone know if their bird-safe plants? I can't seem to find much information online?