They can and many times are kept together. The more important concept is why to NOT do this… In fact I started with both kept together. So here is the rationale why NOT to do it. Koi and Goldfish will interbreed and the result is a pure mutt with absolutely no value. Pond bred koi already have about zero value anyway. read more
Once goldfish have taken hold of pond they can be hard to get rid of - fairly small animals can easily breed and quickly add to the the bio load of a pond. Never put delicate finned or fancy goldfish in a koi pond - koi are just too big of “cows” for these types of fish. read more
Goldfish and koi can coexist just fine, but you will likely have to upgrade your tank to a bigger size if you want to keep the koi fish indoor . Koi can grow very fast so a 29 gallon aquarium will not be sufficient for very long. read more