There's quite a lot of research on this already, as has been noted. There's the idea of 3D-printing organs, for instance. That would naturally be external, and frankly that's all I can foresee for quite a long time coming. The technology right now is to grow externally and implant.

However, you can work with some of the stuff they're doing now with growing external organs. I'm no expert, but I know they use scaffolds and--to simplify it to my own stupid, layperson level--place cells on the scaffold and allow them to grow. It's not exactly like training a plant, but it's something like that, i.e. making it grow in the correct shape. Perhaps some sort of scaffold is used somehow?