Surprise! Banana trees (technically not actually a tree) can make excellent house plants if you have enough light for them! They grow quickly and can get very large indoors in the right conditions. Best yet, they are totally pet safe! So if you've been looking for a large statement plant that cat or dog friendly, this is the one! Banana plants generally have a fast growth rate, and if you choose to grow them outside, they should be planted in the spring. Sadly, banana plants typically won't bear fruit indoors.